i

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

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

Reina Goto, 2012 Royal Institute of Technology (KTH) Department of Civil and Architectural Engineering Division of Structural Engineering and Bridges Stockholm, Sweden, 2012

i

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

v

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

1

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

2

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.

4

5

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

6

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).

11

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

12

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

13

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.

14

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.

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.

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).

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.

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

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.

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

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

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.

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.

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

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

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.

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.

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

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).

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)

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).

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).

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)

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.

36

12000

3000 8000 600400

10000 10001000

Figure 3.7: Side view of the target bridge.

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.

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:

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.

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)

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