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1
8nd International Conference on Physical and Numerical Simulation of Materials Processing, ICPNS’16
Seattle Marriott Waterfront, Seattle, Washington, USA, October 14-17, 2016
Cement asphalt mortar modelling and its influence on highspeed train-bridge system in presence of moderate earthquakes
and service loading
＊
Ling-kun Chen 1, 2 , Li-zhong Jiang3, Jian-min Zeng4, and Ming Zhang1
of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, PR China
2 School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031, PR China
3 National Engineering Laboratory for High Speed Railway Construction, Changsha 410004, PR China
4 School of Material Science and Engineering, Guangxi University, Nanning, Guangxi, 53004, PR China
1 College
ABSTRACT
The cement asphalt mortar (CAM) layers sandwiched between the concrete track slab and concrete base in
China railway track system (CRTS) Ⅱ slab track, act as a cushion to provide the elasticity for train-bridge
system subjected to the earthquakes action and service loading. In this study, based on the multiscale modeling
technology, a high-speed vehicle-ballastless slab track-bridge interaction model is developed. The effects of the
CAM layer on dynamic responses of the system are also analyzed. According to “The tentative requirements for
the cement emulsified asphalt mortar in China railway track system Ⅱ typed slab track of passenger dedicated
railway”, when the Young’s modulus of CAM is 7.0 ~ 10.0GPa, the results indicate that the CAM layer effectively
influence the dynamic response of the train-bridge system and traffic safety.
Keywords: cement asphalt mortar, earthquakes action, service loading, train-bridge system, dynamic response
1.INTRODUCTION
In seismic regions, structures such as high-speed
railway bridge are likely to experience various
seismic events during their service lives. i.e., the
earthquake and the train loading. As a result, the
seismic reliability of non-structures components
including the ballastless slab track may be degraded
from the design standard due to each passing
earthquake.
Figure 1 Structure of CRTS Ⅱ track system
Slab track is an advanced ballastless track form. It
exhibits many applications in high-speed railways in
countries like Japan, Germany, Spain and China due
to its manifold advantages in reducing structure
height, lower maintenance requirements and
increasing service life (Zeng et al. 2015; Yan et al.
2015 ). the socalled CRTS Ⅱ ballastless slab track
system includes three layer of the rail, concrete track
slab and concrete base, the CAM layer is regarded
as an elastic layer bonding the track slab and
concrete base. As shown in Figure. 1, the CAM is
the key component of the slab track, which mainly
consists of cement matrix, asphalt emulsion, fine
aggregate, and a variety of admixtures ( Wang et al,
2012 ). The bonding of the CAM layer between slab
and concrete base layer transmits the longitudinal,
transverse, and vertical force.
According to the split Hopkinson pressure bar test
(Xie et al, 2014), the strength of CRTS Ⅱtype CA
mortar increases gradually with the increasing of
strain-rate compared with those of the CRTS Ⅰtype
CA mortar, However, the increasing rate of strength
of CRTS Ⅱtype CA mortar deceases with the further
increasing of strain-rate. The bonding failure and the
damage caused by the debonding and the gap will
be aggravate subjected to the earthquake. The
mortar debonding will expand and mortar will be
damaged in the beating action because of the high
frequency vibration of track under repeated train
loading after bond failure, which not only affects the
smoothness, safety, and comfort of high-speed
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running, but also does not accord with the
requirement of durability and reliability of high-speed
railway structures. Zhu et al (2014) established a
statistical damage constitutive model for the CAM
layer using continuous damage mechanics and
probability theory, the results indicate that the
proposed model is capable of predicting the damage
evolution of the CAM layer exposed to vehicle
dynamic load. Ren et al (2016) conducted a study on
the criteria for repairing damages of the CAM by
establishing a 3-dimenional (3D) finite element
method (FEM) of the prefabricated framework-type
slab track on the elastic foundation. In order to verify
the calculation results. Zeng et al (2016) carried out
a series of experiments to characterize the dynamic
properties of CAM. The test results indicate that the
compressive strength, the compressive strain, and
the elastic modulus are much more sensitive than
traditional Portland cement mortar.
In the existing literature about the damage of the
CAM during their service lives, little concern has
been engaged to the influence of the earthquake on
the dynamic characteristics of CAM, the performance
of reinforced concrete (RC) structures. More works
are needed to understand the damage of CAM such
as seismic degradation mechanisms in different
structural systems.
This paper investigates the influence of the CAM
layer on the dynamic response of the high-speed
train-CRTS Ⅱ ballastless slab track-bridge system
subjected to seismic events and train loading. In
particular, the focus is on the cushion action of the
CAM layer that are typically the primary supporting,
load transfer, adjustment, and buffer action resisting
components in ballastless slab track system. For this
purpose, a 3D computation model of high-speed
train-CRTS Ⅱ ballastless slab track-bridge system
are developed to predict the effect of the CAM layer
on the dynamic response of the train-bridge system.
In the present study, the high-speed train (motor
car/trailer car) model with 38 degree of freedoms
(DOFs) is built up, based on the inelastic Hertz
contact theory and the Kalker creep theory, the highspeed train-ballastless track/rail-box girder-bearingpier-pier model are established in this paper, the
CRTSⅡballastless slab track and 32m span simplysupported box girder bridge are studied in the model,
the Matlab software is developed to calculated the
seismic responses and train-running safety during
earthquake and service loading. The objective of this
study is to provide a comprehensive modelling
procedure that considers CAM layer to measure the
susceptibility of the train-bridge system under
dynamic conditions. The results establish an
adequate degree of confidence in the use of the
proposed methodology and code in further
parametric analyses and seismic design.
2 PERFORMANCE OF CAM UNDER
EARTHQUAKE AND SERVICE LOADING
The slab track is composed of multiple structures or
components with different materials characteristics.
The performance, strength and structure will impose
an influence on the working conditions of other
components, thus having direct effects on the quality
of train operation (Zhu et al, 2016). CAM is the
adjustment layer and the load-bearing layer of a slab
track structure, which depend on the bonding action
to connect the layered components of the slab track
system. The damage caused by the earthquake will
result in the debonding of CAM layer, therefore, the
cracking, stripping, rupture, excessive plastic
deformation (Dai and Su, 2016).
The impacting of the earthquake on the mortar
surface significantly degrades the mortar stress
conditions and causes degradation of the mortar
material performance. The construction defects will
aggravate the degradation of the stress conditions of
CAM during its service life, further affecting the
durability of the structure.
After damaging the CAM of CRTSⅡballastless slab
track, voids beneath the tracks slab are easy to form,
and disengaging which cause local mutations of the
track stiffness and detrimentally affects the carrying
capacity of the track structure. The high-speed
railways and passenger-dedicated railways require
high durability and reliability of the track structure.
However, the mortar damage or defects can lead to
mutation of track stiffness, which will affect the whole
life cycle of the track system, and then affect the
running safety and riding comfort of the train (Zhai et
al, 2013).
3 3D CAM AND TRAIN-BRIDGE SYSTEM
MODELLING
In this work a 3D coupled dynamics model of a
vehicle and the ballastless slab track is present to
repeatedly calculate the dynamic response. The
longitudinal view of 3D model of train-bridge system
is shown in Figure 2. In the models, the train is
assumed to move in the X direction (railway
direction) and the Y direction is perpendicular to the
railway. The vehicle model is treated as a rigid multibody model with 38 DOFs for a 4-axle train vehicle,
and the train on the bridge is composed of several
tractor cars and trailer cars moving at constant
speed. Each vehicle is a complicated multi-DOFs
vibration system consisting of car-body, bogies,
3
wheel-sets, suspension springs and dashpots. The
car body, bogies and wheel-sets are regarded as
rigid components. Each carbody or bogie has six
DOFs which are designated by the lateral, roll, yaw,
vertical, pitch, and longitudinal displacement. Each
bogie has six DOFs of lateral, roll, yaw, vertical,
pitch, and longitudinal displacement. For each
wheel-set only five DOFs are considered: the lateral,
roll, yaw, vertical and longitudinal displacement. The
connections between car-body and bogies are
represented by linear springs and viscous dashpots
in both vertical and lateral directions, as well as the
connections between bogies and wheel-sets. The
CRTS Ⅱ slab ballastless track on the bridge consists
of rail, fastening system, concrete track slab, CAM
layer, and concrete base. The rails are modeled as
Bernoulli-Euler beams with the vertical, lateral, and
torsion motions of the rails simultaneously. The
concrete track slab and concrete base are described
as elastic rectangle plates according to the elastic
thin slab theory. According to “The tentative
requirements for the cement emulsified asphalt
mortar in China railway track system Ⅱ typed slab
track of passenger dedicated railway”, the
appropriate value of the Young’s modulus of CAM is
7.0 ~ 10.0GPa. The CAM layer is modeled by the
nonlinear spring (Yang et al, 2013), the vertical
stiffness of CAM layer is 6.736×107 N/m base on the
force-displacement relationship of the nonlinear
spring (Liu et al, 2010). when CA mortar layer is
damaged, debonding, or disengaging subjected to
the service loading or combination effect of
earthquake and vehicle loading, to simulate the
contact relationship between the CA mortar and the
track slab, the vertical stiffness of CAM layer can be
taken 0 N/m for the case of debonding, or
disengaging using the ‘‘killed” and ‘‘active” element
technology base on the Ansys software (Ren et al,
2016; Qi et al, 2015), and for the case of damage of
CA mortar, some measures can be adapted by
adjusting the vertical stiffness of CAM layer from 0
N/m to 6.736×107 N/m.
Figure 2 Longitudinal view of 3D model of train-bridge system
In this study, to analyze the influence of CAM layer
on the dynamic response of train-bridge system
under the vehicle and earthquake loading, two fine
analysis model are establish, one is the complete
train-bridge system model including ballastless slab
track, the other has built up the same train-bridge
system model but not considered the CAM layer,
that mean that the stiffness of the vertical spring
between the concrete track slab and concrete base
can be taken the same value as that of the concrete
track slab.
The vehicle and slab track are coupled through the
wheel-rail contact relationship based on the
nonlinear Hertzian contact theory and the modified
Kalker linear creep theory (Zhai et al, 1996). The
dynamic responses of the train-ballastless slab
track-bridge interaction system under the actions of
track irregularities and seismic accelerations can be
computed by using either Newmark-β method or
Wilson-θ method. The FEM program of the trainbridge system TTBDA(Train-track-bridge dynamic
analysis) was developed and verified by the field test
based on the Matlab soft package [Chen et al, 2013],
mounts of calculation were conducted to simulate
the performance of CAM layer under the dynamic
loading.
In present study, the China derailment coefficient
standards were used (TB10621-2009, 2010), i.e., the
wheel lateral to vertical force ratio L/V or Q/P, which
is necessary to permit flange climb derailment, since
the finite element analysis requires a specific
average movement distance or time interval to
calculate the train derailment coefficient.
4. CASE STUDY
A 3D finite element model is used to represent an
example five-span simply supported high-speed
railway bridge in this study. In this study, the X-axis
is defined along the bridge direction, the Y-axis is
perpendicular to the bridge (referring to the
transverse direction), and the Z-axis is the pier
height direction. the span length of box girder is
32m, the material properties of box girder are
Young’s modulus of 30.2 GPa, Poisson’s ratio of
0.15, section area of 8.6597 m 2, moment of inertia of
about the Y axis 80.945 m4, moment of inertia of
about the Z axis 10.811 m4, The box girder is
supported on a 2.2 m × 6.2 m rectangular pier 9.5 m
high. The high-speed train comprises 16 passenger
cars carried by 12 motor cars and 4 trail cars. The
high-speed train running at the speed of 350 km/h is
selected for the case study. The fundamental data of
the motor car and trailer car can refer to Zeng et al
(2015).The present study focus on the influence of
CAM layer on the dynamic response of trains-bridge
system under seismic and the service loading. The
rail is the CHN-60-kg type supported on the upper
concrete track slab of the CRTS Ⅱ type ballastless
4
slab track system, the support interval is 0.625 m in
the rail direction.
The details of the slab track are described as
followed, the CRTS Ⅱ type ballastless slab track
system include a 20-cm-thick concrete track slab for
sustaining the rail, a 3.0-cm-thickCAM layer for
cushioning, and a 20-cm-thick bottom concrete base
for sustaining the track structure on the bridge. The
Young’s modulus and Poisson’s ratio of the concrete
track slab and the concrete base are 35.0 GPa and
0.17, those for the CAM layer are 0.3 GPa and 0.25,
and those for the rail are 200 GPa and 0.3,
respectively. The lateral, longitudinal and vertical
spring stiffness factor of fasteners (between rail and
ballastless track slab) in X, Y and Z directions are
6.0 × 107 N/m, respectively; The lateral, longitudinal
and vertical spring damping factor of fasteners
(between rail and ballastless track slab) in X, Y and
Z directions are 6.0 × 104 N. s/m, respectively; The
lateral, longitudinal and vertical spring stiffness factor
of CAM layer (between ballastless track slab and
base slab) in X, Y and Z directions are 5.0 × 108
N/m, respectively; The lateral, longitudinal and
vertical spring damping factor of CAM layer
(between ballastless track slab and base slab) in X,
Y and Z directions are 7.52 × 104 N. s/m,
respectively; The lateral, longitudinal and vertical
spring stiffness factor of earthwork cloth layer
(between base slab and bridge deck) in X, Y and Z
directions are 8.0 × 108 N/m, respectively; The
lateral, longitudinal and vertical spring damping
factor of earthwork cloth layer (between base slab
and bridge deck) in X, Y and Z directions are 2.0 ×
107 N. s/m, respectively.
Rayleigh damping was used in this study as follows:
 D    M     K 
(1)
where [D], [M], and [K] are damping, mass, and
stiffness matrices, respectively, and the two factors
of  and  for the two natural frequency of 2.678
Hz (the vibration shape is longitudinal vibration of the
bridge) and 3.856 Hz (the vibration shape is lateral
vibration of the box girder) equal 0.455 and 0.00112,
respectively, which gives an approximately 2.3
percent damping ratio at a frequency of 2.678 Hz
and 3.826 Hz.
The maximum accelerations in the analysis are
normalized as 0.2g (g = the acceleration of gravity).
which is completely equivalent to the so-called
Hazard level Ⅱ (Design Level Earthquake) —
Earthquake at this level of hazard are normally
assumed to have a 10% probability of being exceed
in 50 years.
The track irregularity in this study is Germanic lowdisturbance spectrum. As are shown in Figure 3,
z(x), y(x) and r(x) are the vertical, align (lateral) and
cross-lever (torsional) track irregularities adopted in
the following calculation, respectively.
y(x)/(mm)
(a) 8.0
4.0
0.0
-4.0
-8.0
0
500
1000
x/(m)
1500
2000
2500
0
500
1000
x/(m)
1500
2000
2500
0
500
1000
x/(m)
1500
2000
2500
y(x)/(mm)
(b) 8.0
4.0
0.0
-4.0
-8.0
r(x)/(mm)
(c) 6.0
4.0
2.0
0.0
-2.0
-4.0
-6.0
Figure 3 Track irregularities: (a) track vertical profile irregularity; (b) track alignment irregularity; and (c) track cross-level
irregularity
5
4.1. EFFECT OF CAM ON THE DYNAMIC
BAHAVIOR OF TRAIN-BRIDGE SYSTEM
MODELLING UNDER SERVICE LOADING
In general, for the train-ballastless slab track-bridge
system model, the stiffness, mass and damp
matrices would change since the CAM mortar layer
was filled between concrete track slab and concrete
base, and furthermore, the assembled global
stiffness, mass and damp matrice of train-bridge
system would accordingly changed. The peak
response of bridge for vehicle-bridge system with
12m pier height, 32m span and 350km/h traveling
speed were shown in Table 1. The forces and
displacement were compared at the following
locations and directions in the train-bridge system,
those responses were monitored at the selective
piers and spans, i.e., the third span in present study.
Table 1 The peak response of bridge for vehicle-bridge system with 12m pier height, 32m span and 350km/h travelling speed
Dynamic responses
With CAM layer
Without CAM layer
Lateral displacement at mid-span of box girder / (mm)
0.177
0.113
Vertical displacement at mid-span of box girder / (mm)
2.3
1.7
Lateral displacement at top of pier / (mm)
0.285
0.146
Lateral acceleration at mid-span of box girder / (m/s2)
0.304
0.114
Vertical acceleration at mid-span at box girder / (m/s2)
0.708
0.504
Lateral acceleration at top of pier / (m/s2)
0.216
0.120
Lateral acceleration of trailer car / (m/s2)
0.525
0.537
Vertical acceleration of trailer car / (m/s2)
0.694
0.496
trailer car of trailer car
0.321
0.369
trailer car of trailer car / (kN)
17.68
20.89
trailer car of trailer car
0.594
0.371
layer was not considered, compared with those
without considering the CAM layer, the train-running
safety index of train get greater for the high-speed
train-ballastless track - bridge model in which the
ballastless track restraint is considered; the results
indicate that the influence of the CAM layer cannot
ignore.
0.3
0.3
0.2
0.2
Derailment coefficient
2
Lateral acceleration/(m/s )
The effects of the CAM layer on the dynamic
response of the train-bridge system subjected to the
service loading were calculated through the 3D
models including the CRTS Ⅱ ballastless slab track
system described in section 3. As indicated in Figure
4, the dynamic response of bridge get smaller for the
high-speed train-rail-bridge model in which CAM
0.1
0.0
-0.1
With CAM Layer
Without CAM Layer
0.1
0.0
-0.1
-0.2
-0.2
-0.3
With CAM Layer
Without CAM Layer
-0.3
0
2
4 Times/(sec) 6
8
-0.4
10
(a) Lateral acceleration at the mid-span of box girder
0
2
4 Time/(sec) 6
8
10
(b) Derailment coefficient of the third tractor car
Figure 4 Dynamic responses time history curve of train - bridge system
In general, for the train-ballastless slab trackbridge system model, the stiffness, mass and damp
matrices would change since the CAM mortar layer
was filled between concrete track slab and concrete
base, and furthermore, the assembled global
stiffness, mass and damp matrice of train-bridge
system would accordingly changed. The CAM layer
will be damaged even disengaged from the ballasted
slab track system under the dynamic loading, the
variation of the stiffness of the CAM layer will change,
then, the global stiffness of the train-bridge system,
6
which result in the different response according to
the dynamic differential equation.
4.2. EFFECT OF CAM ON THE DYNAMIC
BAHAVIOR OF TRAIN-BRIDGE SYSTEM
MODELLING UNDER SEISMIC NAD
SERVICE LOADING
In Figure 5, the effects of the CAM layer on the
seismic response of the train-bridge system
subjected to the earthquake action. As can be seen
from Figure, take the El Centro record of empire
valley 1940 earthquake for a example, the dynamic
response of bridge get smaller and the train-running
safety index of train get greater for the vehicle- rail-
bridge model in which the ballastless track restraint
is not considered and stiffness of the bridge get
greater; the influence law of dynamic response of the
vehicle- rail-bridge system without earthquake action
were be broken under the strong seismic excitation,
the seismic response of the system are suited to the
spectrum characteristics of ground motion, the
seismic response of the system were larger
compared with the high-speed train-ballastless trackbridge system, it having a distinct characteristic of
the pulse-excitation, the ballastless track restraint
can significantly affected the train-running safety
index of the vehicle, the ballastless track can
effectively improve the train-running safety behavior
of vehicle with/without earthquake action.
3.00
With CAM Layer
Without CAM Layer
2.25
0.4
Derailment coefficient
Lateral acceleration/(m/s2)
0.0
1.50
0.75
0.00
-0.75
-0.4
-0.8
-1.2
-1.6
-2.0
With CAM Layer
Without CAM Layer
-2.4
-1.50
0
2
4
Time/(sec)
6
8
10
(a) Lateral acceleration at the mid-span of box girder
0
2
4
Time/(sec)
6
8
10
(b) Derailment coefficient of the third tractor car
Figure 5 Seismic response of the train-bridge system subjected to the El Centro record of empire valley 1940 earthquake
5. CONCLUSIONS
In the present study, the high-speed train model with
38 DOFs is built up, based on the inelastic Hertz
contact theory and the Kalker creep theory, the highspeed train-ballastless track/rail-box girder-bearingpier-pier model are established, the
CRTSⅡballastless slab track and 32m span simplysupported box girder bridge are studied in the model,
the program TTBDA is developed to calculated the
dynamic responses and train-running safety during
earthquake and service loading.
When the Young’s modulus of CAM is 7.0 ~
10.0GPa, the results indicate that the CAM layer
effectively influence the dynamic response of the
train-bridge system and traffic safety. The results
show that seismic degradation in CAM can
significantly increase the seismic vulnerability of RC
highway bridges.
ACKNOWLEDGES
The research was supported by China Postdoctoral
Science Foundation Grant No. 2016M592695
and2015M581702, Natural Science Foundation of
Jiangsu Province, P R China Grant No.BK20161337
and Financial Aid Scheme for Selecting and Training
Project of High-level Talents of the 10th “Top 6
Talent Peak” in Jiangsu Province P R China Grant
No. 2013-JZ-005. Those supports are gratefully
acknowledged.
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