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Seismic performance of a bridge subjected to far-field
ground motions by a Mw 9.0 earthquake and near-field
ground motions by a Mw 6.9 earthquake
REINA GOTO
Master of Science Thesis Stockholm, Sweden 2012
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Seismic performance of a bridge subjected to far-field ground motions by a Mw 9.0 earthquake and near-field ground motions by a Mw 6.9 earthquake
Reina Goto
June 2012 TRITA-BKN. Master Thesis 358 ISSN 1103-4297 ISRN KTH/BKN/EX-358-SE
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Reina Goto, 2012 Royal Institute of Technology (KTH) Department of Civil and Architectural Engineering Division of Structural Engineering and Bridges Stockholm, Sweden, 2012
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Preface
This Masters thesis was initiated with the help of Kawashima Research Group at the Department of Civil Engineering at the Tokyo Institute of Technology, Tokyo Tech, and was carried out at the Department of Civil and Architectural Engineering at the Royal Institute of Technology, KTH.
First and foremost, I would like to give my sincere gratitude to Professor Kazuhiko Kawashima, Tokyo Tech, and Assistant Professor Hiroshi Matsuzaki, Tohoku University. I would like to thank Professor Kawashima for his great support and advices. I would like to thank Assistant Professor Matsuzaki for helping me with all my questions and to understand the seismic design methods and the dynamic response analysis better.
I would like to thank my supervisor Post Doctor Nora Ann Nolan, KTH, for her great support and giving me valuable advices.
I would also like to thank my examiner Professor Raid Karoumi, KTH, for showing great interest and being very helpful during the course of the thesis.
Special thanks to the members of the Kawashima Research Group, Tokyo Tech, for all their help and for sending me papers and files needed for the research.
Stockholm, June 2012
Reina Goto
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Abstract
In the last two decades, two major earthquakes have occurred in Japan: the 1995 Kobe
earthquake and the 2011 Great East Japan earthquake. In the 2011 Great East Japan
earthquake, many bridge structures were destroyed by the tsunamis, but it is
interesting to study the ground motion induced damage and also how this earthquake
differed from the one in 1995. In this thesis, the seismic response of a bridge designed
according to the current Japanese Design Specifications was evaluated when it is
subjected to near-field ground motions recorded during the 1995 Kobe earthquake and
far-field ground motions recorded during the 2011 Great East Japan earthquake. For
this purpose, a series of nonlinear dynamic response analysis was conducted and the
seismic performance of the bridge was verified in terms of its displacement and
ductility demand.
It was found from the dynamic response analysis that the seismic response of the target
bridge when subjected to the ground motions from the 2011 Great East Japan
earthquake was smaller than during the 1995 Kobe earthquake. Although the ground
motions from the 2011 Great East Japan earthquake were very strong, they were not
as strong as the ground motions from the 1995 Kobe earthquake. The results obtained
in this thesis clarify the validity of the Type I and Type II design ground motions. The
target bridge used in this thesis was designed according to the post-1990 design
specifications and showed limited nonlinear response when subjected to the different
ground motions which shows how efficient the enhancement of the seismic performance
of bridges has been since the 1990s.
Keywords: seismic performance, dynamic response analysis, far-field ground motions, near-field ground motions
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Notations
Main notations
Ah Sectional area of each lateral confining reinforcement
Aw Sectional area of reinforcing bars
b Width of the column section
cc Cyclic loading effect factor
cD Damping modification factor
ce Effective height factor
cpt Modification factor depending on the longitudinal tensile reinforcement ratio
cR Factor depending on the bilinear factor
cs Response modification factor
cZ Zone modification factor
d Effective length of lateral confining reinforcement
D Effective height of the column section
dR Residual displacement developed at a column
dRa Allowable residual displacement at a column
dRa,LG Allowable residual displacement in the longitudinal direction
dRa,TR Allowable residual displacement in the transverse direction
du Ultimate displacement of column
dy Yield displacement of column
Ec Youngs modulus of concrete
Edes Descending gradient
fc Strength of concrete
fcc Strength of confined concrete
fck Design strength of concrete
fsy Yield strength of reinforcement bars
gal Measure of acceleration (1 gal = 1 cm/s2)
h Height of the column/effective height of the column section
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khc0 Standard modification coefficient
khc Design horizontal seismic coefficient
Lp Plastic hinge length of column
My0 Initial yield moment
Mu Ultimate moment
P Lateral strength
Pa Lateral capacity of a column
Ps Shear strength of a column
Ps0 Shear strength under static loading of a column
Pu Ultimate lateral strength of a column
r Bilinear factor
s Spacings of lateral confining reinforcement
S Response acceleration spectrum for the Level 1 earthquake ground motion
S0 Standard acceleration spectra for Level 1 earthquake ground motion
SI Response acceleration spectra for Type I ground motion
SII Response acceleration spectra for Type II ground motion
Sc Shear capacity resisted by concrete
Si Standard acceleration response spectra
Ss Shear capacity resisted by transverse reinforcement
T Fundamental Period
Ti Natural periods
W Equivalent weight
Wp Weight of the column
WU Weight of part of the superstructure supported by the column concerned
Shape factor/safety factor
Shape factor
c Strain of concrete
cc Strain of concrete under the maximum compressive stress
s Volumetric ratio of lateral confining reinforcements
sy Yield point of the reinforcements
Damping ratio
a Design displacement ductility factor of a column
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R Response displacement ductility factor of a column
c Average shear stress that can be borne by concrete
u Ultimate curvature
y Yield curvature
Abbreviations
AIS Arc Information Systems
EW East-West horizontal component of ground motion
JRA Japan Road Association
LG Longitudinal
NIED National Research Institute for Earth Science and Disaster Prevention
NS North-South horizontal component of ground motion
PGA Peak ground acceleration
RC Reinforced concrete
SPL Seismic Performance Level
TR Transverse
UD Up-Down vertical component of ground motion
WSJ The Wall Street Journal
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Contents
Preface ..................................................................................................................... i
Abstract ................................................................................................................. iii
Notations ................................................................................................................ v
1 Introduction .................................................................................................... 1
1.1 Aim and scope of thesis .............................................................................. 1
1.2 Organization of thesis ................................................................................ 3
2 Background and previous studies ..................................................................... 5
2.1 Seismic history of Japan ............................................................................ 5
2.1.1 1995 Kobe earthquake .................................................................... 6
2.1.1.1 Shear failure of RC columns ............................................ 6
2.1.1.2 Collapse of steel columns ................................................. 7
2.1.1.3 Damage to unseating prevention devices ......................... 8
2.1.1.4 Damage to steel bearings ................................................. 8
2.1.2 2011 Great East Japan earthquake................................................. 9
2.1.2.1 Bridges designed before 1990 ......................................... 10
2.1.2.2 Bridges that had been retrofitted or designed after 1990 10
2.2 History of seismic design of bridges in Japan ............................................ 11
2.3 Current seismic design ............................................................................. 15
2.3.1 Basic principles ............................................................................ 15
2.3.2 Analytical methods to verify the seismic performance .................. 18
2.3.3 Design of RC columns .................................................................. 20
2.4 Previous studies ....................................................................................... 25
3 Methodology .................................................................................................. 27
3.1 Ground motions ....................................................................................... 27
3.2 Response acceleration spectra .................................................................. 32
3.3 Target bridge ........................................................................................... 34
3.3.1 General ........................................................................................ 34
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3.3.2 Reinforced concrete columns ........................................................ 37
3.3.2.1 Design details of the RC columns .................................. 37
3.3.2.2 Design process of the columns ....................................... 37
3.3.3 Bearings ....................................................................................... 42
3.3.4 Foundations ................................................................................. 47
3.4 Finite element analysis program TDAP III .............................................. 48
3.5 Analytical idealizations ............................................................................ 49
3.5.1 Mass idealizations ........................................................................ 49
3.5.2 Damping idealizations .................................................................. 50
3.5.3 Structural elements ...................................................................... 51
3.5.3.1 Fiber elements ............................................................... 52
3.5.3.2 Linear springs ................................................................ 54
3.5.3.3 Material properties ........................................................ 55
3.6 Analysis using TDAP III ......................................................................... 58
3.6.1 Self-weight analysis ...................................................................... 58
3.6.2 Eigen value analysis ..................................................................... 58
3.6.3 Dynamic response analysis ........................................................... 59
3.7 Sensitivity analysis .................................................................................. 59
3.8 Convergence study ................................................................................... 61
3.8.1 Time step ..................................................................................... 61
3.8.2 Number of fiber elements ............................................................. 62
4 Results ........................................................................................................... 65
4.1 Mode shapes and natural period of the bridge .......................................... 65
4.2 Comparison between the 1995 and 2011 earthquake ................................ 66
4.2.1 Relative response displacement at the top of column .................... 67
4.2.2 Relative response displacement at the deck .................................. 70
4.2.3 Moment vs. curvature hysteresis .................................................. 74
4.2.4 Stress vs. strain hysteresis ............................................................ 76
4.2.5 Verification of seismic performance .............................................. 79
4.2.5.1 Ductility capacity and demand ...................................... 79
4.2.5.2 Residual displacement ................................................... 80
5 Conclusions and suggestions for further research .............................................. 81
5.1 Conclusions.............................................................................................. 81
5.2 Suggestions for further research ............................................................... 82
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References .............................................................................................................. 83
Appendix A Ground motions UD............................................................................. 86
Appendix B Calculations RC column ....................................................................... 88
Appendix C Mode shapes ........................................................................................ 92
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Chapter 1
Introduction
Japan is situated on a region where several tectonic plates meet, which is why Japan is
extremely prone to earthquakes. There have been many earthquakes in the past and
many lessons to be learnt alongside it. Japan has made huge investments to improve
buildings and infrastructures to mitigate seismic damage. The Japanese seismic design
codes have been revised several times and revisions are sure to appear in the future.
On March 11th 2011, Japan was hit by a huge earthquake called 2011 Great East Japan
earthquake. It was the biggest earthquake ever recorded in Japan and it was apparent
that the country was not prepared for the kind of damages that followed the
earthquake. Not only did this earthquake cause immense damage and casualties, but it
also caused the biggest nuclear disaster since Chernobyl in 1986 to further grieve the
people of Japan. Many bridge structures were destroyed by the tsunamis, but it is
interesting to see how the ground motions of the earthquake damaged these bridge
structures. In the context of seismic design of bridges, perhaps there are lessons to be
learnt from this earthquake. To mitigate seismic damage of bridges, it is important to
find out how this earthquake differed from other earthquakes in the past and whether
or not the Japanese Seismic Design Specifications for bridges need to be revised.
1.1 Aim and scope of thesis
The aim of this thesis is to evaluate the seismic response of a bridge designed by the
current Japanese seismic design codes when it is subjected to ground motions recorded
during the two major earthquakes that have occurred in Japan in the last two decades:
the 2011 Great East Japan earthquake and the 1995 Kobe earthquake. For this
purpose, a series of nonlinear dynamic response analysis of a bridge is conducted. The
seismic performance of the bridge is then verified in terms of its displacement and
ductility demand.
First, the seismic history of Japan will be studied to understand the damages that have
occurred in the past. The 1995 Kobe earthquake and the 2011 Great East Japan
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earthquake will be studied in more detail, since the ground motion records from these
earthquakes will be used in this thesis. The current Design Specifications and how it
has changed over the years since its first publication will also be studied. A literature
review to find any information that is relevant to this thesis will be conducted and
presented.
Ground motion records from the 1995 Kobe earthquake and the 2011 Great East Japan
earthquake will be evaluated to see differences in the ground motion characteristics.
Also response acceleration spectra for the ground motion records will be analyzed to
see and compare the intensity and predominant period of each ground motion. A
bridge based on the Japanese Seismic Design Specifications is used to conduct a
dynamic response analysis using a Japanese finite element analysis program called
TDAP III. The seismic response and seismic performance of the bridge when subjected
to different ground motions will then be evaluated.
General steps in this thesis are:
1. Evaluate how the two earthquakes differ in character. The ground motion
characteristics will be compared as well as its response acceleration spectra.
2. Conduct dynamic response analysis using TDAP III.
3. Compare the seismic response of the bridge and evaluate its seismic performance
based on the results from the dynamic response analysis.
4. Discuss whether or not the current Japanese Seismic Design Specifications for
bridges are sufficient for an earthquake with a different character than the 1995
Kobe earthquake such as the 2011 Great East Japan earthquake.
Several assumptions and simplifications were made in this study. The target bridge
was taken from an example book issued by the Japan Road Association and it was
designed based on nonlinear static analysis. In reality nonlinear dynamic response
analysis should be conducted when designing a bridge, but in this case the bridge was
designed based on only nonlinear static analysis for simplicity.
In the dynamic response analysis, the difference in the arrival time of the earthquake
ground motions were not considered since the length of the target bridge is only 0.2 km.
The difference in the arrival time should be considered for longer bridges. Also, torsion
and shear deformation were not considered in this analysis.
The damping ratios of the elastomeric bearings, soil springs, and structural
components of the bridge were assumed using values from the Japanese Design
Specifications (JRA, 2002). These damping ratios were assumed since the aim of this
study is to compare the seismic response of the target bridge when subjected to
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different ground motions and to find a precise damping is not of interest. Damping of
the bridge structure was idealized using Rayleigh damping (see Section 3.5.2 for the
calculations of the Rayleigh coefficients and the damping curve).
1.2 Organization of thesis
Chapter 2 gives some background information necessary for this thesis. A short
summary of the seismic history of Japan is presented and the 2011 Great East Japan
earthquake and 1995 Kobe earthquake are presented in detail. The history of seismic
design in Japan is summarized linking the revisions of the Seismic Design
Specifications to damages that were observed after some of the major earthquakes.
Also the current Japanese Seismic Design Specifications are presented. Previous
studies of relevance are discussed. The methods of analysis, the target bridge, and the
bridge model are presented in detail in Chapter 3. The results of the analysis are
presented in Chapter 4 and are analyzed. In Chapter 5, the conclusions that were
deduced from this study are presented and any suggestions for future research are
discussed.
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Chapter 2
Background and previous studies
2.1 Seismic history of Japan
Japan has a long history of earthquakes and some of the more significant earthquakes,
in terms of seismic design, will be presented here. In the early 1900s when seismic
effects were either not or poorly considered in design, the 1923 Kanto earthquake with
a moment magnitude of 7.9 occurred in the Tokyo-Yokohama area (Kawashima, 2000).
This earthquake caused large scale damage to buildings and infrastructure, where
bridges collapsed due to tilting, overturning, and settlement of the foundations. Due to
this earthquake, the importance of considering seismic effects in design was recognized
for the first time (Kawashima, 2011).
In 1964, an earthquake with a moment magnitude of 7.5 occurred in Niigata which
came to be called the 1964 Niigata earthquake. Many bridges were damaged or
collapsed due to soil liquefaction and it was at this time that the actual term
liquefaction was first coined (Kawashima, 2011). It became evident after this
earthquake that soil liquefaction needed to be considered in seismic design. However,
at that time, further research to understand the mechanism of liquefaction was needed
before implementing any countermeasures. Bridges were also damaged by large relative
displacements of the decks, which inspired the development and implementation of
unseating prevention devices.
After the 1964 Niigata earthquake and up to the early 1990s, several big earthquakes
occurred. However, the damages in these earthquakes were quite limited due to
changes in seismic design practices. It was not until 1995, that a big earthquake that
would greatly change the seismic design practices in Japan occurred. This was the 1995
Kobe earthquake and it had a great impact on the seismic design of bridges. Even to
this day, ground motions from this earthquake are used for dynamic response analysis
of bridges. Since the ground motions from the 1995 Kobe earthquake are used in this
thesis, it is presented more in detail in Section 2.1.1. Similarly, the recent 2011 Great
East Japan earthquake is presented in detail in Section 2.1.2, since ground motions
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from this earthquake are also used in this thesis and the damages that occurred need to
be thoroughly described.
2.1.1 1995 Kobe earthquake
In 1995, 17th of January, the 1995 Kobe earthquake occurred at Kobe and Awaji Island,
in southern Japan. This earthquake had a moment magnitude of 6.9 and near-field
ground motions were recorded. Thousands of deaths and extensive damage to buildings
and infrastructures were reported. Many bridges suffered damage, where 9 highway
bridges collapsed or nearly collapsed and 16 bridges were severely damaged. The four
major types of damages that were observed are summarized below, based on the
lecture notes from Seismic design of urban infrastructure (Kawashima, 2011).
2.1.1.1 Shear failure of RC columns
Figure 2.1 shows the collapse of the 18-span Fukae Viaduct of the Hanshin Expressway
in Kobe. This viaduct was designed based on the 1964 Design Specifications that will
be presented later in Section 2.2. During the earthquake, the RC columns which were
9.9 m to 12.4 m tall with a diameter of 3.1 m to 3.3 m were damaged by severe flexural
and diagonal cracks that developed 2.5 m above the footing. This was where one third
of the longitudinal reinforcement bars terminated. Since the amount of tie bars were
not enough, premature shear failure shown in Figure 2.2 also occurred in the columns.
These damages occurred due to the deficiencies in design. For instance, the allowable
shear stress was overestimated and the development length of the longitudinal bars
was insufficient. This kind of failure occurred in several other bridges as well such as in
the Takashio Viaduct which was built according to the 1971 Design Specifications.
Figure 2.1: The collapse of the Fukae Viaduct. (Kawashima, 2011)
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2.1.1.2 Collapse of steel columns
Steel columns collapsed in numerous bridges and an example of this is Tateishi Viaduct
at the Hanshin Expressway. A picture of a collapsed column from this viaduct is shown
in Figure 2.3. This viaduct was also built based on the seismic coefficient method from
the 1964 Design Specifications. The steel columns were built between two RC columns
at the sides and lateral beams were constructed to support two side decks. To reduce
damage of the steel columns in the event of an automobile accident, the inside of the
columns were filled with weak concrete from the bottom up to a height of 2.3 m.
During the earthquake, local buckling of web and flange plates and rupture of the
welded corners at the bottom of the columns occurred. This caused the bearing
capacity of the columns to decrease in the lateral and vertical directions. The columns
became vulnerable to the dead weight of the decks and started to settle. When this
happened, the decks in the center started to buckle and in the end the steel columns
collapsed.
Figure 2.3: Collapse of a steel column of the Tateishi Viaduct. (Kawashima, 2011)
Figure 2.2: Premature shear failure of column of the Fukae Viaduct.
(Kawashima, 2011)
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2.1.1.3 Damage to unseating prevention devices
Damage to various types of unseating prevention devices was observed. This happened
since the design force of the devices was too small. The design force was calculated by
multiplying the static reaction force by a seismic coefficient of 0.3 to 0.4. In the
Nishinomiya Bridge of the Hanshin Expressway, one of the approach spans collapsed
(Figure 2.4.a). The main bridge and the approach spans were connected by plate-type
restrainers (Figure 2.4.b). During the earthquake, the fixed bearings of the main bridge
failed and caused the bridge to displace, pulling the approach span. Eventually the
approach spans dislodged from its supports and collapsed since the unseating
prevention devices could not support it without the help of the supports.
a) Collapse of an approach span (Nishinomiya Bridge)
b) Failure of a plate-type restrainer
Figure 2.4: Damage to unseating prevention devices (Kawashima, 2011).
2.1.1.4 Damage to steel bearings
Extensive damage to steel bearings was also observed in this earthquake (Figure 2.5).
Prior to the 1995 Kobe earthquake, steel bearings were thought to restrict extensive
damage to the bridge substructures. However, after observing the damage caused by
the failure of steel bearings, it became apparent that steel bearing were one of the main
causes of the extensive damage that occurred (Kawashima, 2011). This is because steel
bearings are weak for shock and have insufficient strength and length of movement.
Apart from the three above mentioned damages, damage to bridge foundations were
also observed. However these damages were minor compared to the rest of the
structural components. Damage caused by soil liquefaction was also observed in the
form of settlements and tilting of foundations and bridge substructures. Foundations
were also damaged by large lateral spreading which was caused by soil liquefaction.
The Japanese Design Specifications were revised in 1996 due to the poor seismic
performance of bridges in this earthquake. The revisions that were made in the Design
Specifications will be presented in Section 2.2.
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a) Failure of steel pin bearing b) Failure of steel bearing Figure 2.5: Failure of steel bearings (Kawashima, 2011).
2.1.2 2011 Great East Japan earthquake
On March 11, 2011 a devastating earthquake of moment magnitude 9.0 occurred off
the Pacific coast, northeast of Japan. This was the biggest earthquake ever recorded in
Japan and was named the 2011 Great East Japan earthquake. This earthquake
lasted for more than 300s and strong ground motion accelerations were recorded in
several areas. The coastal regions of northeast Japan were hit by tsunamis after the
earthquake which caused severe damage to buildings and infrastructures, human
injuries, and casualties. The earthquake was felt all the way down to the Kanto region
and extensive soil liquefaction occurred in the Tokyo Bay area as well as in Chiba
Prefecture where damage such as settlements of buildings and uplift of sewage
manholes were observed (Ishihara, 2012).
The tsunamis swept away and damaged several bridges along the coast, but damage to
bridges which was induced by ground motions was less extensive. However, according
to a study by Kawashima et al. (2011) and Kawashima (2012), bridges that were
designed based on the design codes prior to the 1990 and 1995 Design Specifications
and were not retrofitted were damaged due to the ground motions. Bridges that had
been retrofitted or built according to the post 1990 Design Specifications showed only
minor damage or no damage at all. This showed that seismic retrofitting and the
improvements that had been made in the Design Specifications were efficient. The
bridge damage that was observed after the 2011 Great East Japan earthquake is
presented within two categories: bridges designed pre-1990 and post-1990.
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2.1.2.1 Bridges designed before 1990
The same type of damage to RC columns as in the 1995 Kobe earthquake occurred,
which was mentioned in Section 2.1.1. In the Esaki Ohashi Bridge, damage to the RC
columns was observed which can be seen in Figure 2.6.a. This type of damage occurred
in bridges that were designed before the 1990s and had an overestimated shear
capacity and not enough development length of the longitudinal bars. Kunita Ohashi
Bridge was also designed prior to the 1990s and had not been retrofitted at the time of
the earthquake. This bridge was closed for service after the earthquake, since its steel
bearings were damaged (Figure 2.6.b) and shear cracks had developed in the RC
columns. The information on the damage on the Esaki Ohashi Bridge and the Kunita
Ohashi Bridge were obtained from a study by Hoshikuma et al. (2012).
a) RC columns (Esaki Ohashi Bridge)
b) Steel bearings (Kunita Ohashi Bridge)
Figure 2.6: Damage to bridges designed prior to 1990-design codes (Hoshikuma et al., 2012).
2.1.2.1 Bridges that had been retrofitted or designed after 1990
Bridges that had been retrofitted after the 1995 Kobe earthquake, by for example steel
jacketing of RC columns and replacing steel bearings with elastomeric bearings,
showed in most cases no signs of damage. Bridges that were designed according to the
post-1990 Design Specifications were not damaged or showed only minor damages.
However, some bridges suffered severe damage to its elastomeric bearings and dampers.
One of these bridges was the Tobu Viaduct in Sendai, where elastomeric bearings
ruptured (Kawashima, 2012). Figure 2.7.a show how the rupture of the bearings caused
the bridge deck to offset in the transverse direction by 0.5 m and Figure 2.7.b show
that the rubber layers detached from the steel plates and ruptured. Some possible
reasons to why this damage occurred could be because of a design miss or that the
interaction of adjacent decks was not properly considered (Takahashi, 2012 and
Kawashima, 2012). Damage was also observed in the attachments and anchors of
dampers (Figure 2.8).
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a) Offset due to rupture of elastomeric bearings
b) Rupture of elastomeric bearing
Figure 2.7: Damage of elastomeric bearings in the Tobu Viaduct (Kawashima, 2012).
a) Damage of anchors b) Damage of attachment
Figure 2.8: Damage of attachments and anchors of dampers (Takahashi, 2012).
2.2 History of seismic design of bridges in Japan
The revisions and history of the Japanese Design Specifications for seismic design of
bridges will be presented in this subsection, based on lecture notes from Seismic
Design of Urban Infrastructures (Kawashima, 2011) and papers by Professor
Kawashima (Kawashima, 2000 and Kawashima, 2006).
In 1926, three years after the 1923 Great Kanto earthquake, the first Japanese seismic
provisions for highway bridges were published. In these specifications, the seismic
coefficient method using a seismic coefficient of 0.1 to 0.3 was included and only the
requirement of seismic lateral force of 20% gravity force was presented. Design
specifications of steel highway bridges were included in 1939 and were revised twice
afterwards in 1956 and 1964. At this time, earthquake engineering was still something
new and under progress, so the seismic design requirements in these specifications were
far from what they are now. It was not until the 1964 Niigata earthquake that
engineers realized the need for major improvements of the seismic provisions. After
NEXCO East
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observing the damages caused by the 1964 Niigata earthquake, a completely renewed
seismic design provisions, Guide Specifications for Seismic Design of Highway
Bridges, were issued in 1971. Some of the improvements and changes that were made
are presented below:
The lateral force should be calculated by considering the zone, importance of
the bridge, and ground condition in the seismic coefficient method. Also the
structural response should be considered in the modified seismic coefficient
method.
Since many bridges were damaged by soil liquefaction in the 1964 Niigata
earthquake, the evaluation of soil liquefaction was included. However, the
mechanism of soil liquefaction was unknown at that time so design procedure
for liquefaction could not be included in 1971.
The need for unseating prevention devices were recognized in this earthquake so
several types of unseating prevention devices such as steel plate connectors and
cable restrainers were developed.
Many independent methods for the design of substructures had been developed
and these methods were unified as Guide Specifications of Substructures
between 1964 and 1971. This resulted in the development of new types of
foundations which helped reduce the damage of the bridge foundations.
In 1980, the above Guide Specifications for seismic design and substructures were
revised. These specifications were written as Part V Seismic Design and Part IV
Substructures in the Design Specifications of Highway Bridges. Parts I to III were
the General Aspects, Steel Bridges, and Concrete Bridges respectively. A
method for the design of foundations in liquefying soils and an updated version of the
evaluation method for predicting soil liquefaction were added in Part V. In Part IV,
the allowable shear stress for concrete was reduced since this was overestimated in the
past. The anchoring length of the reinforcement bars from the footings was increased
to 20 times the diameter of the bars and the length equivalent to the effective width of
the column.
The Design Specifications were revised again in 1990. In this revision, the following
changes were made:
The seismic coefficient method and the modified seismic coefficient method were
unified.
For the first time, to enhance the ductility of bridge columns, the check of the
strength and ductility of the reinforced concrete columns was included. The
nonlinear behavior of a bridge was to be checked after the structural members
yielded. The Type I ground motion of the standard lateral force coefficient in
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Figure 2.9 was introduced for the ductility check. This ground motion
represents the ground motions that are assumed to have occurred in the 1923
Kanto earthquake. Type II ground motion was included in the later revisions.
The static frame method was introduced so that the lateral force distribution of
a multi-span continuous bridge could be evaluated. Through this method, the
three dimensional behavior of a bridge could be considered in the equivalent
static analysis.
Figure 2.9: The standard lateral force coefficient (Kawashima, 2000).
As previously mentioned, even though strong earthquakes occurred several times in the
1980s and the beginning of 1990s, the damages were quite limited due to the
improvements that had been made in seismic design. Therefore, the damages that
resulted from the 1995 Kobe earthquake were somewhat shocking. 40 days after this
earthquake, the Guide Specifications for reconstruction and repair of highway bridges
which suffered damage in the 1995 Kobe earthquake was issued to guide the
reconstructions of the bridges that were damaged in this earthquake. This Guide
Specifications came to be used in new constructions of bridges as well, until a revised
version of the Design Specifications came out in 1996. In this Guide Specifications, a
requirement for the design of a plastic hinge at the bottom of columns and the effect of
lateral confinement was included. Also, the Type II ground motion in Figure 2.9 was
included which represents the ground motions recorded in the 1995 Kobe earthquake.
In 1996, the Design Specifications from 1990 were fully revised and included the above
mentioned 1995 Guide Specifications. Some of the major changes that were made are
the following:
The previous check of the ductility of the reinforced concrete columns was
improved to the ductility design method. Although the seismic coefficient
method was still in use, revisions in the Design Specifications were made so that
all the structural components that are vulnerable to seismic effects are to be
checked with the ductility design method.
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The type of ground motion (Type I and Type II) is to be considered in
determining the design ductility factor and shear strength of a bridge column,
and also in determining the soil strength for liquefaction.
Specifications for the dynamic analysis were revised, where revisions were made
in the analytical models and methods, and safety checks. Also the input
earthquake ground motions to be used in dynamic analysis were specified.
Requirements for the residual displacement of a column after an earthquake
were included and this had to be checked for bridges in the important bridge
category.
An unseating prevention system was introduced and design loads and methods
were specified. The function of the unseating prevention devices was also
clarified.
Elastomeric bearings were recommended to be used as opposed to steel bearings
which have several deficiencies.
The seismic design treatment of soil liquefaction was reviewed and is to be used
as a seismic design method in places where liquefaction is likely to occur. The
seismic design treatment of lateral spreading caused by soil liquefaction was also
defined.
Since 1996, the Design Specifications have been revised in 2002. Revisions were made
based on the Performance-based design concept, where requirements of the necessary
performance and verification of policies are clearly stated. Some of the changes that
were made are summarized in the following points:
Seismic performance requirements of highway bridges, principles of seismic
performance verifications, and the determination concept of design earthquake
ground motion were clearly defined. These specifications were based on concepts
from the performance-based design.
The methods of verifying seismic performance were rearranged to two design
methods: Static analysis and Dynamic analysis. The verification method for
the latter analysis was defined in detail and its applicability was improved.
A method to verify the seismic performance of abutment foundations on
liquefiable grounds was included for the first time. Similarly, a method to verify
the seismic performance of steel and concrete superstructures was introduced.
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15
The current Design Specifications will be presented in detail below in Section 2.3. The
Design Specifications have been revised again in March 2012, but this has not been
published yet. Therefore the revisions that were made in 2012 will not be discussed in
this study and the Design Specifications from 2002 will be used.
2.3 Current seismic design
In this section, the Design Specifications from 2002 (JRA, 2002) will be presented. The
Design Specification of Highway Bridges is issued by the Japan Road Association
(JRA) and consists of five parts: Part I Common, Part II Steel Bridges, Part III
Concrete Bridges, Part IV Substructures, and Part V Seismic Design. Some key parts
of the Part V Seismic Design will be presented in this section based on lecture notes
from Seismic Design of Urban Infrastructures (Kawashima, 2011), papers by
Professor Kawashima (Kawashima, 2004 and Kawashima, 2006), and the English
translation of the Part V Seismic Design by JRA (JRA, 2002).
2.3.1 Basic principles
In seismic design, a bridge must be designed so that its required seismic performance is
satisfied during an earthquake. The seismic performance of a bridge is determined by
the importance of the bridge and also the levels of design ground motion that is likely
to occur at the site of construction. Furthermore, the topographical-, geological-, soil-,
and site conditions must be considered in seismic design.
Table 2.1 shows the seismic performance matrix. Bridges are categorized into two
types; either Type A or Type B. Type A are bridges with standard importance and
Type B are bridges with high importance. The importance of the bridge is classified by
using Table 2.2. The type of design ground motions is divided into two levels: Level 1
Earthquake which is ground motions with a high probability occurrence and the Level
2 Earthquake which is ground motions with a low probability occurrence. The design
response acceleration spectra for these design ground motions can be seen in Figure
2.10. The Level 1 Earthquake is the ground motions that are developed in moderate
earthquakes and the ground motion used in conventional elastic design method. The
Level 2 Earthquake includes two types of ground motions: Type I and Type II. Type I
represents ground motions developed in interplate-type earthquakes with a large
magnitude, which targets the ground motions that most likely occurred in the 1923
Kanto earthquake. Type II represents ground motions developed in inland-nearfield-
type earthquakes and the ground motions from the 1995 Kobe earthquakes are typical
targets of this type. Type I ground motion is characterized as having a large amplitude
and longer duration, while Type II is characterized as having strong accelerations and
shorter duration.
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16
Depending on the bridge type and design ground motions, the Seismic Performance
Level (SPL) needs to be ensured. SPL 1 requires bridge damage to be prevented, which
means that the main functions of the bridge must be maintained during an earthquake.
SPL 2 requires limited damage in order to recover its function, meaning that the bridge
should only suffer limited damage and be able to recover within a short time. In SPL 3,
critical damage of the bridge must be prevented.
a) Level 1 Earthquake
b) Level 2 Earthquake (Type I) c) Level 2 Earthquake (Type II)
Figure 2.10: Design acceleration spectra (JRA 2002, Kawashima 2004).
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17
Table 2.1: Classification of importance of bridges (JRA, 2002).
Type Definitions
A bridges
Bridges other than Type B bridges
B bridges
Bridges of National expressways, urban expressways, designated city expressways, Honshu-Shikoku highways, and general national highways.
Double-deck bridges and overbridges of prefectural highways and municipal roads, and other bridges, highway viaducts, etc., especially important in view of regional disaster prevention plans, traffic strategy, etc.
Table 2.2: Seismic performance matrix (JRA, 2002).
Type of Design Ground Motions Standard Bridges
(Type-A)
Important Bridges (Type-B)
Level 1 Earthquake: Ground Motions with High Probability to Occur
SPL 1: Prevent Damage
Level 2 Earthquake: Ground Motions with Low Probability to Occur
Interplate Earthquakes (Type-I)
SPL 3: Prevent Critical Damage
SPL 2: Limited Damage for Function Recovery
Inland Earthquakes (Type-II)
The loads and load combinations that need to be considered in the seismic design of
bridges are the primary and the secondary loads. These loads are shown below in Table
2.3. The combination of the loads should be: primary loads + effects of earthquake.
The loads and its combinations should be determined to give the most unfavorable
condition. Depending on the site of construction, not all loads will be considered.
According to JRA, the live load does not need to be considered in seismic design. This
is because the live load varies temporally and spatially and during an earthquake, the
probability of a full live load occurring is small.
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18
Table 2.3: Primary and secondary loads to be considered in design (JRA, 2002).
Primary loads Secondary loads
Dead load Effects of earthquake Prestress force Effect of creep of concrete Effect of drying shrinkage of concrete Earth pressure Hydraulic pressure Buoyancy or uplift
The effects of earthquake include:
Inertia force due to the dead weight of the structure
Earth- and hydrodynamic pressure during an earthquake
Effects of liquefaction and liquefaction-induced ground flow
Ground displacement during an earthquake
2.3.2 Analytical methods to verify the seismic performance
In the Japanese Design Specifications, to verify the seismic performance of a bridge,
the limit state of each structural member should be defined considering the limit states
of the bridge. If the response of the structural members due to the design ground
motions does not exceed the determined limits, the seismic performance is verified. The
limit states of the bridge are the Seismic Performance Levels 1, 2, and 3 which were
briefly mentioned in Section 2.3.1. These limit states are determined considering the
requirements summarized in Table 2.4 from the Design Specifications.
Table 2.4: Establishing the Seismic Performance Levels (JRA, 2002).
Seismic Performance Level
Limit States
SPL 1 Mechanical properties of the bridges maintained within the elastic ranges
SPL 2 Only the structural member in which the generations of plastic hinges are allowed deforms plastically within a range of easy functional recovery
SPL 3 Only the structural member in which the generations of plastic hinges are allowed deforms plastically within a range of the ductility limit of the member
The design earthquake ground motions, and structural type and limit states of the
bridge must be considered when choosing the appropriate analytical method to verify
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19
the seismic performance. The appropriate analytical method is either a static or
dynamic analysis. For a proper evaluation of the seismic performance, the nonlinear
behaviors of a member might need to be considered so an appropriate analytical
method must be chosen to account for these properties. See Table 2.5 for the required
analytical method depending on the complexity of seismic behavior and the SPLs.
When determining the seismic performance by a static analysis, the loads that are
caused by an earthquake are added statically to the bridge. The dynamic structural
characteristics in the elastic range are considered in the seismic coefficient method
when verifying for SPL 1. In the seismic coefficient method, loads that have been
calculated by using the seismic coefficient are applied to the bridge statically. From
this, the resultant deformations and sectional forces are evaluated. In ductility design
method, the deformation properties and dynamic strength of the nonlinear zone of a
structure are considered. This method is used for the verification of SPL 2 and SPL 3.
In both the seismic coefficient method and design ductility method, the dynamic
seismic forces are changed to a static force by using the seismic coefficient.
When a dynamic method is used for seismic performance verification, the maximum
response values of the bridge obtained from the dynamic analysis must be smaller than
the allowable values. The response spectrum or time-history response analysis methods
are commonly used in dynamic analysis. The most suitable method and model are
chosen considering the purpose of the analysis and the earthquake ground motion level.
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20
Table 2.5: Relation between Complexity of Seismic Behavior and Design Methods
Applicable to Seismic Performance Verification (JRA, 2002).
2.3.3 Design of RC columns
RC columns are designed so that it satisfies the following requirement in Equation 2.1.
WkP hca
(2.1)
ppU WcWW
(2.2)
where, Pa is the lateral capacity of a column, khc is the design horizontal seismic
coefficient, W is the equivalent weight, WU is the weight of part of the superstructure
supported by the column concerned, Wp is the weight of the column, and cp is the
equivalent weight coefficient (0.5 for bending failure or shear failure after flexural
yielding and 1.0 for shear failure).
Dynamic characteristics of bridges
Bridges without complicated seismic behavior
Bridges with plastic hinges & yielded sections, and bridges not applicable of the Energy Conservation Principle
Bridges of likely importance of higher modes
Bridges not applicable of the Static Analysis Methods
Seismic Performance to be verified
SPL 1 Static analysis
Static analysis Dynamic analysis
Dynamic analysis
SPL 2 & SPL 3 Static analysis
Dynamic analysis Dynamic analysis
Dynamic analysis
Examples of applicable bridges
Other than bridges shown in the right columns
Bridges with rubber bearing to disperse seismic lateral forces
Seismically-isolated bridges
Reinforced Concrete rigid-frame bridges
Bridges with steel piers likely to generate plastic hinges
Bridges with long natural periods
Bridges with high piers
Long-span bridges such as cable-stayed bridges and suspension bridges
Deck-type & half through-type arch bridges
curved bridges
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21
The design horizontal seismic coefficient is calculated using Equation 2.3:
zhczshc ckcck 4.00
(2.3)
where, cs is the response modification factor, cz is the zone modification factor (= 0.7,
0.85, or 1.0 depending on the zone), and khc0 is the standard modification coefficient.
The response modification factor, needed to calculate the above mentioned
requirement, may be calculated using Equation 2.4, which assumes the equal energy
principle. The equal energy principle is more conservative than the equal displacement
principle.
12
1
a
Sc
(2.4)
where, a is the design displacement ductility factor of a column.
In order for the RC column to perform according to its expected seismic performance,
the response displacement ductility factor, r , should be smaller than the design
displacement ductility factor, a . However it may not be greatly smaller, since this
would result in an overestimation of the response modification factor.
A plastic hinge, which can show ductile behavior when it is subjected to repeated
alternate deformations, can be defined at the bottom of each RC column. The plastic
hinge region dissipates energy through plastic deformation without collapsing the
remaining structural members and by designing these plastic hinges in a proper way
can allow the damage that occurs after an earthquake to be localized and repaired
more easily (Long and Bergad, 2004). The plastic hinge length is determined in the
Japanese Design Specifications using Equation 2.5, however it must be in the interval
DLD P 5.01.0 . In analytical purposes, the plastic hinge is a virtual concept which
allows the displacement due to plastic deformation at the defined plastic hinge region
to be evaluated more easily (Kawashima, 2011).
DhLP 1.02.0 (2.5)
where, h is the height of the column and D is the effective height of the column section.
For every column which has a defined plastic hinge, a fiber element analysis is
performed at the plastic hinge regions assuming a stress vs. strain relationship for
concrete and reinforcing bars. An elastic-perfect plastic model is used to idealize the
stress vs. strain relationship of reinforcing bars. The stress vs. strain relationship of
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22
confined concrete is based on Hoshikuma et al. (1997) which is presented below in
Equation 2.6 to Equation 2.11.
cccdescc
n
cc
ccc
c
Ef
nE
f
1
11
ccc 0 (2.6)
cuccc
cccccccc
fE
En
(2.7)
sysckcc fff 8.3
(2.8)
ck
sys
ccf
f 033.0002.0
(2.9)
sys
ckdes
f
fE
2
2.11
(2.10)
018.04
sd
Ahs
(2.11)
where, fc is the strength of concrete, fcc is the strength of confined concrete, fck is the
design strength of concrete, fsy is the yield strength of reinforcement bars, c is the
strain of concrete, cc is the strain of concrete under the maximum compressive stress,
Ec is the Youngs modulus of concrete, Edes is the descending gradient, and are
shape factors, and s is the volumetric ratio of lateral confining reinforcements, Ah is
the sectional area of each lateral confining reinforcement, and s and d are the spacings
and effective length of lateral confining reinforcement. The shape factors are obtained
by the following Table 2.6.
Table 2.6: Shape factors for circular and rectangular columns.
Circular Rectangular 1.0 0.2 1.0 0.4
According to the Design Specifications, the volumetric ratio of lateral confining
reinforcements should be smaller than 1.8%. This recommendation was proposed since
there must be a limitation to how much the ductility capacity of a column should be
enhanced by just increasing the amount of lateral reinforcement. If the restraining
force of concrete is too high, the plastic hinge region will generally become smaller
when the column is subjected to repeated plastic deformations. This can cause the
longitudinal reinforcements to fracture leading the column to reach the ultimate state.
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23
The ultimate displacement, du, is defined as the displacement at the gravity center of a
superstructure when the compression strain of the concrete at the out-most
reinforcements reaches the ultimate strain,cu , in Equation 2.12. The ultimate strain is
dependent on the type of ground motion.
des
cccc
cc
cu
E
f2.0
Type I ground motion (2.12)
Type II ground motion
The ultimate displacement of a column, du, is found using Equation 2.13 (Priestly and
Park 1987 and Priestly et al. 1996).
2
p
pyuyu
LhLdd
(2.13)
where, dy is the yield displacement, u is the ultimate curvature, y is the yield
curvature, h is the height of the column, and Lp is the length of the plastic hinge.
The shear strength of a RC column, Ps, is evaluated according to the following
equations:
scs SSP (2.14)
dbcccS cptecc (2.15)
a
dAS
syw
s15.1
cossin
(2.16)
where, Ps is the shear strength, Sc and Ss is the shear capacity resisted by concrete and
transverse reinforcement, c is the average shear stress that can be borne by concrete,
cc is the cyclic loading effect factor which can be obtained from Table 2.7, ce is the
effective height factor, cpt is the modification factor depending on the longitudinal
tensile reinforcement ratio, b is the width of the column section, h is the effective height
of the column section, Aw is the sectional area of reinforcing bars with interval a and
angle and sy is the yield point of the reinforcements.
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24
Table 2.7: The cyclic loading effect factor, kc.
Load Type kc
Static loading 1.0
Type I ground motion 0.6
Type II ground motion
0.8
The failure mode of a column is classified as either flexural failure, shear failure after
flexural yielding, or shear failure and this is to be evaluated using Equation 2.21. The
failure mode is decided based on the ultimate lateral strength Pu, shear strength Ps,
and shear strength under static loading Ps0 of a RC column.
su PP : Flexural failure
(2.17) 0sus PPP : Shear failure after flexural yielding
us PP 0 : Shear failure
The lateral strength of the RC column, Pa, is calculated depending on the failure mode
using Equation 2.18:
0s
u
a
P
PP
: Flexural failure + shear failure after flexural yielding (2.18)
: Shear failure
The ductility capacity of the RC column, a , is also calculated depending on the
failure mode:
1
1y
yu
ad
dd
: Flexural failure (2.19)
: Shear failure after flexural yielding + shear failure
where, du and dy are the ultimate and yield displacement, is the safety factor which is determined based on the Seismic Performance Level and the type of ground motion.
See Table 2.8 for the safety factors.
Table 2.8: Safety factor .
Seismic Performance Level
Type I ground motions
Type II ground motions
SPL 2 3.0 1.5
SPL 3 2.4 1.2
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25
The residual displacement dR developed at a column, should satisfy the requirement in
Equation 2.20, which states that the residual displacement should be smaller than the
allowable residual displacement dRa. The allowable residual displacement is 1% of the
distance from the bottom of the column to the height of inertia force of the
superstructure.
RaR dd (2.20)
yRRR drcd 11 (2.21)
1
2
12
a
sR
Pg
S
(2.22)
where, dRa is the allowable residual displacement, r is the bilinear factor (ratio of yield
stiffness and post-yield stiffness), cR is a factor depending on the bilinear factor, R is
the response displacement ductility factor.
2.4 Previous studies
An evaluation of the seismic performance of RC bridge piers designed by the pre- and
post- 1995 Kobe earthquake was conducted by Kawashima (2000). A cantilever RC
column of a four-span continuous bridge was used in this study which was designed by
the 1964, 1980, 1990, and 1995 Design Specifications respectively for comparison. The
four columns were assumed to have the same conditions except for changes in the size
and reinforcement of the column. After evaluating the columns based on the 1995
Design Specifications, it was found that the column designed by the 1964 Specifications
was the only one that failed in shear. However the column of the 1980 Specifications
failed in flexure and the 1990 column suffered extensive flexural damage. The 1995
column did not suffer damage or fail in either of the two above-mentioned ways. To
evaluate the seismic performance of the columns, a dynamic response analysis using a
ground motion record from the 1995 Kobe earthquake was conducted for all the
columns except for the 1964 column since it failed in shear. Through this study, it has
been found that the column based on the 1964 Design Specifications overestimates the
allowable shear stress and together with the inadequate anchorage of the
reinforcements, makes this column vulnerable to damage. The 1980 column was also
vulnerable to flexural damage when subjected to the ground motion type recorded in
the 1995 Kobe earthquake.
A study by Matsuzaki (2012) evaluating the intensity of the ground motions from the
2011 Great East Japan earthquake based on nonlinear seismic response of standard
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26
bridges was recently published. Response acceleration spectra are usually used to
evaluate the intensity of ground motions, however intensity evaluated by nonlinear
response of bridges can be more reliable. In this study, three bridges designed by the
Japanese Design Specifications were used. All three bridges were a three-span
continuous plate girder bridge with four RC columns and five elastomeric bearings on
each column, but the dimensions of the RC column are different in each of the bridges.
In the nonlinear response analysis, the bridges were subjected to four ground motion
records from the 2011 Great East Japan earthquake. Also, one ground motion from the
2008 Iwate-Miyagi earthquake and two ground motions from the 1995 Kobe
earthquake were used for comparison. It was found from the analysis that although the
response acceleration of the ground motions recorded in the 2011 Great East Japan
earthquake were high at a period shorter than 0.3 s, the seismic response of the bridges
was small when subjected to these ground motions. JMA Furukawa and JR Takatori
had similar response accelerations at the natural period of the target bridges, but the
peak deck displacement under JR Takatori was much larger than under JMA
Furukawa. This type of difference in response cannot be predicted by only looking at
the response acceleration spectra. JMA Furukawa ground motion record from the 2011
Great East Japan earthquake developed the largest response out of the ground motions
from this earthquake, but the response was smaller than that of the JR Takatori
ground motion record from the 1995 Kobe earthquake. According to this study, the
ground motion records from the 2011 Great East Japan earthquake can be said to be
smaller than the Type II design ground motion. Finally it was concluded that the
seismic response of bridges evaluated by nonlinear response analysis are different than
the expected response based on only response acceleration spectra, so the intensity of
ground motions should be evaluated based on nonlinear response analysis of several
target bridges with different structural properties.
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27
Chapter 3
Methodology In this chapter, the ground motions from the 2011 Great East Japan earthquake and
the 1995 Kobe earthquake that will be used in this study will be presented. The ground
motion characteristics will be evaluated as well as the response acceleration spectra.
The target bridge that will be used in this study and a detailed design process of the
RC columns will be presented to understand how the Seismic Design Specifications
introduced in Section 2.3 are used in the design process. The idealizations that were
made in modeling the target bridge will be presented. To find the seismic response of
the target bridge when subjected to the ground motions, three types of analysis (self-
weight, Eigen value, and dynamic response analysis) are conducted using a Japanese
finite element analysis program which will be explained later in this chapter. At the
end of this chapter, a sensitivity analysis and convergence study that was conducted
when choosing certain values that will be used in the analysis will be presented.
3.1 Ground motions
In this study, three far-field ground motions recorded during the 2011 Great East
Japan earthquake and two near-field ground motions recorded during the 1995 Kobe
earthquake are used in the dynamic response analysis. The ground motion records from
the 2011 Great East Japan earthquake were obtained from the Kyoshin Net,
abbreviated K-Net, which is a Japanese strong motion seismograph network that
provides access to strong motion data. K-Net can be accessed online from the National
Research Institute for Earth Science and Disaster Preventions website (NIED, 2011).
The strong motion data are obtained from 1000 observatories set up throughout Japan.
In this study, since the ground motion records from K-Net did not start from zero
acceleration, the data was adjusted to zero start. The ground motions from the 2011
Great East Japan earthquake has a long duration and in order to reduce the
computational time for the analysis, the first 10 s were cut since cutting the beginning
by this amount only caused an insignificantly small change in the response of the
target bridge. See Section 3.8 for the Sensitivity analysis.
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28
Figure 3.1 to Figure 3.2 shows the NS and EW components of the ground motions for
Tsukidate, Furukawa, and Sendai from the 2011 Great East Japan earthquake. These
ground motions had two peak accelerations between 30 s and 100 s. Although the
ground motions lasted for more than 300 s, only the acceleration lasting for 60 s which
include the two peaks is shown here. Figure 3.3 and Figure 3.4 shows the NS and EW
components of the ground motions for JR Takatori and JMA Kobe from the 1995 Kobe
earthquake. These ground motions had a shorter duration of about 30 s, while only 20 s
which include the peak is shown here. See Appendix A for the UD direction.
The ground accelerations from the 2011 Great East Japan earthquake were much
stronger than the ground accelerations from the 1995 Kobe earthquake, except for
Furukawa. Table 3.1 shows the peak ground acceleration (PGA) for each of the five
ground motion records. Tsukidate had the strongest PGA for both the NS and EW
components. The PGA for the NS component is 27.0 m/s2 which are more than 229 %
higher than the PGAs of the 1995 Kobe earthquake ground motions. Sendai has a PGA
of 15.2 m/s2 for the NS component which is less than the PGA for Tsukidate, but
higher than the remaining ground motions.
The far-field ground motions from the 2011 Great East Japan earthquake are
characterized by long duration and repetitious ground motions, while the near-field
ground motions from the 1995 Kobe earthquake are characterized by short duration
and long pulse accelerations which is also referred to as killer pulse accelerations.
Near-field ground motions are commonly characterized as having these long pulse
accelerations which contribute to the decrease of the response modification factor and
increase the residual displacement of the bridge column after an earthquake
(Kawashima, 2011). Also the intensity of near-field ground motions can be amplified
due to directivity.
Table 3.1: Peak ground accelerations.
Earthquakes Ground motions
NS (m/s2)
EW (m/s2)
2011 Great East Japan
Tsukidate 27.0 12.7
Sendai 15.2 9.8
Furukawa 4.4 5.7
1995 Kobe JR Takatori 6.4 6.7
JMA Kobe 8.2 6.2
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29
-30
-20
-10
0
10
20
30
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) a) Tsukidate record
-10
-5
0
5
10
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) b) Furukawa record
-20
-10
0
10
20
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) c) Sendai record
Figure 3.1: Ground motion records from the 2011 Great East Japan earthquake (NS).
-
30
-30
-20
-10
0
10
20
30
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) a) Tsukidate record
-10
-5
0
5
10
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) b) Furukawa record
-20
-10
0
10
20
30 40 50 60 70 80 90 100
Acc
eler
atio
n (
m/s
2)
Time (s) c) Sendai record
Figure 3.2: Ground motion records from the 2011 Great East Japan earthquake (EW).
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31
-10
-5
0
5
10
0 5 10 15 20
Acc
eler
atio
n (
m/s
2)
Time (s) a) JR Takatori record
-10
-5
0
5
10
0 5 10 15 20
Acc
elera
tio
n (
m/s
2)
Time (s) b) JMA Kobe record
Figure 3.3: Ground motion records from the 1995 Kobe earthquake (NS)
-10
-5
0
5
10
0 5 10 15 20
Acc
elera
tio
n (
m/s
2)
Time (s) a) JR Takatori record
-10
-5
0
5
10
0 5 10 15 20
Acc
elera
tio
n (
m/s
2)
Time (s) b) JMA Kobe record
Figure 3.4: Ground motion records from the 1995 Kobe earthquake (EW)
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32
3.2 Response acceleration spectra
The response acceleration spectrum for the five ground motions was found since the
response acceleration spectra can show the intensity and predominant period of the
ground motions. In this study, the response acceleration spectrum for each ground
motion was calculated using a program run by FORTRAN. This program performs an
iteration of dynamic analysis based on the Newmark-beta method. The damping ratio
is assumed to be 0.05 and the natural period ranges from 0.1 s to 4 s. The average
acceleration method is used, meaning that the factors 5.0 and 25.0 were used.
Figure 3.5 shows the response acceleration spectra for Tsukidate, Furukawa, Sendai,
JR Takatori, and JMA Kobe for the NS, EW, and UD components respectively. The
response acceleration for the UD component is considerably smaller than the NS and
EW component, apart from the Tsukidate record that has a peak response acceleration
of 106.5 m/s2 at a period of 0.12 s. Tsukidate ground acceleration had the highest PGA
of 27.0 m/s2 for the NS component which resulted in an extremely high response
acceleration of 128.8 m/s2 at 0.24 s. However, although Tsukidate had extremely high
response acceleration at a period range less than 0.5 s, they were less than 5 m/s2 at a
period range over 0.5 s. For a period range over 1 s, JR Takatori has the highest
response acceleration out of the five ground motions. At a period range between 1 s
and 1.5 s, the response acceleration is over 20 m/s2 with the highest response of 21.5
m/s2 at 1.23 s (NS).
Table 3.2 shows the response acceleration of the ground motions at periods of 1.17 s
and 1.00 s for the NS and EW component respectively. 1.17 s and 1.00 s correspond to
the natural period of the target bridge in the longitudinal and transverse direction
respectively (see Section 4.1 for the mode shapes and natural periods of the bridge
obtained from the Eigen value analysis). JR Takatori has the largest response
acceleration of 20.55 m/s2 in the NS component and also in the EW component with a
response acceleration of 13.71 m/s2. Out of the ground accelerations from the 2011
Great East Japan earthquake, Furukawa has the highest response acceleration for the
natural periods of the bridge.
By comparing the response acceleration spectra of the ground motions from the 2011
Great East Japan earthquake with the design response acceleration spectra of the
Level 2 earthquake ground motions presented in Section 2.3 (Figure 2.10), it can be
observed that the intensity of the ground motions from the 2011 Great East Japan
earthquake are generally smaller than the Type I and Type II design ground motions at
a period around 1 s. It should be noted that most of the ground motions from the 2011
Great East Japan earthquake were recorded at stiff sites so a direct comparison to the
Type I and Type II design ground motions are difficult (Kawashima, 2012 and
Matsuzaki, 2012).
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33
Table 3.2: Response acceleration at period 1.17 s (NS) and at 1.00 s (EW).
Ground motions
NS (m/s2)
EW (m/s2)
Tsukidate 3.65 3.45
Sendai 9.88 5.80
Furukawa 11.64 9.58
JR Takatori 20.55 13.71
JMA Kobe 9.81 12.08
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3 3.5 4
Tsukidate
Furukawa
Sendai
JMA Kobe
JR Takatori
Res
po
nse
Acc
eler
atio
n (
m/s
2)
Natural Period (s)
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3 3.5 4
Tsukidate
Furukawa
Sendai
JMA Kobe
JR Takatori
Res
po
nse
Acc
eler
atio
n (
m/s
2)
Natural Period (s) a) NS component b) EW component
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3 3.5 4
Tsukidate
Furukawa
Sendai
JMA Kobe
JR Takatori
Res
po
nse
Acc
eler
atio
n (
m/s
2)
Natural Period (s) c) UD component
Figure 3.5: Comparison of the response acceleration (damping ratio 0.05).
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34
3.3 Target Bridge
The target bridge in this study is a typical example of a bridge design based on the
Japanese Design Specifications. The target bridge was taken from an example book on
seismic design of highway bridges issued by the Japan Road Association (JRA, 1997)
and it was designed based on nonlinear static analysis (ductility design method) which
was presented in Section 2.3. It is preferable to conduct a nonlinear dynamic response
analysis when designing a bridge, but in this case the bridge was designed based on
only nonlinear static analysis for simplicity. The following design details and
calculations in the following subsections are all translated into English from the
example book mentioned above.
3.3.1 General
Figure 3.6 and Figure 3.7 shows the target bridge. The bridge is a five span continuous
girder bridge with a span length of 40 m and a total length of 200 m. Each deck is 40 m
long and 12 m wide. The height of the columns is 10.0 m and the height of the
abutments is 8.15 m. The lower 0.5 m of the abutments and columns as well as the
footings is beneath ground. The footings have a height of 2.2 m and 2 m for the
columns and abutments respectively. The cross sections of the footings are 25.85.8 m
for the columns and 2125.8 m for the abutments.
The columns P1-P4 have a plastic hinge of 1.1 m at the bottom of the columns. The
length of the plastic hinge is calculated by Equation 2.9 which was previously
mentioned in Section 2.3.4. In the case of the target bridge, the plastic hinge length of
the column is calculated as follows:
78.12.21.00.102.0 PL (3.1)
The Design Specifications requires that the plastic hinge length satisfies the
requirement: DLD P 5.01.0 . Since the calculated plastic hinge length is larger than
0.5D, the length of 0.5D will be used.
1.12.25.05.078.1 D (3.2)
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35
12200
P1A1 P2 P3 P4 A2
10000
D1 D2 D3 D4 D5
200000
40000 40000 40000 40000 40000
Figure 3.6: The target bridge.
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36
12000
3000 8000 600400
10000 10001000
Figure 3.7: Side view of the target bridge.
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37
3.3.2 Reinforced concrete columns
Based on the dimensions and design of reinforcements that will be presented in this
section, the seismic performance of the RC column was evaluated with the ductility
design method. A column is analyzed independently of the other bridge members and
the procedures of the ductility design method from the Design Specifications will be
presented here.
3.3.2.1 Design details of the RC columns
The bridge columns are constructed of reinforced concrete and have a rectangular cross
section with an effective height of 2.2 m and width of 5 m. The columns have an
overhang at the top. Details and cross sections of the column can be seen in Figure 3.8
to Figure 3.11. The columns have longitudinal reinforcement bars of diameter 32 mm
and are double reinforced in the longitudinal direction of the bridge. Tie bars of 16 mm
with a spacing of 150 mm are set and cross bars with the same dimension are set inside
the core concrete.
3.3.2.2 Design process of the columns (ductility design method)
The RC columns are designed according to the Design Specifications that were
presented in Section 2.3.4. In general, the following steps are taken for both the bridge
and perpendicular bridge axis:
1. Calculate the ultimate flexural lateral capacity, Pu, and the shear capacity, Ps,
of the column.
2. Determine the failure mode. Lateral capacity, Pa, and design displacement
ductility factor, a , are determined based on the failure mode.
3. Check that the lateral capacity fulfills the proposed requirement stated in the
Design Specifications.
4. If the bridge is a Type B bridge, check that the residual displacement, Ra , is
within the safety limits stated in the Design Specifications.
These steps are repeated four times, twice for the bridge axis direction for Type I and
Type II ground motion and twice again for the perpendicular bridge axis direction for
Type I and Type II ground motion. Since the same equations are used each time, only
the calculation procedure for the bridge axis direction, Type I ground motion, will be
presented here. Please see Appendix B for the other three calculations. The results of
all four calculations will be summarized in the end of this subsection.
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38
Calculations for the bridge axis direction
The tie reinforcement ratio was calculated to be 0.53% by using Equation 3.3. The tie
reinforcement ratio is smaller than the recommended 1.8%. The stress-strain curve of
the concrete was found for this tie reinforcement ratio, where the compressive strain
was
cc = 0.00300 and the ultimate compressive strain was cu = 0.00443.
018.000530.00.1000.15
986.144
sd
Ahs
(3.3)
where, Ah is the sectional area of each lateral confining reinforcement, and s and d are
the spacings and effective length of lateral confining reinforcement.
Calculations based on Type I ground motion:
Based on the stress-strain curve obtained previously, the ultimate strain of concrete
becomes 00300.0 cccu for the Type I ground motion. Since the RC column has
double longitudinal reinforcements, the ultimate stage is reached when the concrete
compression strain at the outmost reinforcements reaches the ultimate strain. Initial
yield is reached when the tensile strain of the outmost reinforcements reaches the yield
strain,sy , and the moment and curvature from the yield stage are obtained from an
elasto-plastic envelop curve at the elastic limit point (Nagata and Sasaki, 2006).
The moment vs. curvature relation of the column cross section was obtained from the
Design Specifications (Part V, Ch.9.3) to determine the lateral force vs. lateral
displacement relation at the gravity center of the superstructure. See Table 3.3 for the
values of moment, curvature, lateral strength, and lateral displacement.
Table 3.3: Moment vs. curvature relation of the column base (Type I ground motion).
Stage Moment (tf m)
Curvature (1/m)
Lateral strength
(tf)
Lateral displacement
(m)
Cracking Mc = 1296.6 410016.1 c Pc = 129.7 -
Initial yield My0 = 4373.6 3
0 10052.1y Py0 = 437.4 0308.00 yd
Yield My = 4956.6 310192.1 y Py = 495.7 0349.0yd
Ultimate Mu = 4956.6 210417.1 u Pu = 495.7 1697.0ud
The lateral strength, yield curvature, and the displacement at the yield and ultimate
stages are evaluated using the following equations:
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39
0
0
y
y
uy
M
M
(3.4)
h
MP
(3.5)
0
0
y
y
uy d
M
Md
(3.6)
2
p
pyuyu
LhLdd
(3.7)
where, P is the lateral strength, My0 and Mu are the initial yield and ultimate moment,
h is the height of the column (= 10 m), du and dy are the ultimate and yield
displacement, y and u are the yield and ultimate curvature, and Lp is the plastic
hinge length (= 1.1 m).
The shear strength of the column is calculated using the Equations 3.8 to 3.10. Note
that the equations are similar to Equations 2.18 to 2.20 from Section 2.3.4, but with
some minor differences in the equation for conversion of units.
tf
dbcccS cptecc
5.224030.2000.53.3327.1845.06.010
10
(3.8)
tf
a
dAS
syw
s 7.4200.1515.110
030.23000916.11
15.110
cossin
(3.9)
tfSSP scs 1.6467.4205.224
(3.10)
where, Ps is the shear strength, Sc and Ss is the shear capacity resisted by concrete and
transverse reinforcement, c is the average shear stress that can be borne by concrete,
cc is the cyclic loading effect factor which can be obtained from Table 2.10 in Section
2.3.4, ce is the effective height factor, cpt is the modification factor depending on the
longitudinal tensile reinforcement ratio, b is the width of the column section, h is the
effective height of the column section, Aw is the sectional area of reinforcing bars with
interval a and angle and sy is the yield point of the reinforcements.
Now that the ultimate lateral strength, Pu, and the shear strength, Ps, of the column
are obtained, the failure mode is decided. Since the ultimate lateral strength is smaller
than the shear strength, and the cracking strength is smaller than the ultimate lateral
strength, the failure mode is evaluated to be flexural failure.
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40
tfPtfP
tfPtfP
uc
su
7.4957.129
1.6467.495
Since the failure mode was flexural failure, the design displacement ductility factor, a ,
is calculated according to the following Equation 3.11:
29.20349.00.3
0349.01697.011
y
yu
ad
dd
(3.11)
where, du and dy are the ultimate and yield displacement, and is the safety factor.
The safety factor, , is taken from Table 2.11 from Section 2.3.4 as 3.0 since the
target bridge is in the important bridge category and the calculations are based on
Type I ground motion.
The equivalent seismic coefficient is obtained through the ductility design method
based on the Design Specifications Part V. The design seismic coefficient khc is found to
be 0.85, so the equivalent seismic coefficient becomes 0.45, see below for calculations.
85.0hck
(3.12)
45.0129.22
85.0
12
a
hche
kk
4.00.14.04.0 zhe ck
(3.13)
The tributary weight of the superstructure-column system, W, is calculated as in the
following:
tfWcWW PPU 1.8062.3465.00.633
(3.14)
where, WU is the weight of the superstructure carried by a column, WP is the weight of
the column body, and cP is the tributary weight calculation coefficient for flexural
failure (=0.5).
The lateral capacity of the RC column, Pa is the ultimate lateral strength:
tfPP ua 7.495
(3.15)
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41
The lateral capacity of the column satisfies the requirement presented below:
tfWkhe 7.3621.80645.0
tfWktfP hea 7.3627.495 !OK (3.16)
According to the Design Specifications, the residual di
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