Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

MECHANISM OF SEISMIC RESPONSE OF A PC
CABLE-STAYED BRIDGE SUBJECTED TO A
LONG-PERIOD SEISMIC EXCITATION
Gaku SHOJI1, Jun KITAHARA2, Atsushi KOJIMA3, Toshiyuki KANAKUBO4,
Katsuyuki SHIMIZU5 and Yuki SAKAI6
1

Associate Professor, Graduate School of Systems and Information Engineering, University of Tsukuba(1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan)
E-mail: gshoji@kz.tsukuba.ac.jp
2
Bureau of Sewerage, Tokyo Metropolitan Government(2-8-1 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8001, Japan)
E-mail: Jun_Kitahara@member.metro.tokyo.jp
3
Graduate School of Systems and Information Engineering, University of Tsukuba(1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan)
E-mail: kojima@kz.tsukuba.ac.jp
4
Associate Professor, Graduate School of Systems and Information Engineering, University of Tsukuba(1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan)
E-mail: kanakubo@kz.tsukuba.ac.jp
5Former Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba(1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan)
6
Associate Professor, Graduate School of Systems and Information Engineering, University of Tsukuba(1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan)
E-mail: sakai@kz.tsukuba.ac.jp

In this study, the mechanisms associated with the seismic response of a long-period structure when subjected to a long-period seismic excitation are clarified. A typical scale cable-stayed bridge withprestressed concrete girders (PC cable-stayed bridge) was selected for analysis. First, we simulated longperiod components of the ground motion at the site of the Ji-Lu Bridge, which was damaged in the 1999
Chi-Chi, Taiwan earthquake, and the damage of the bridge was assessed by nonlinear seismic analysis
using the simulated ground excitations. Second, shaking table tests of a model PC cable-stayed bridge
were carried out, in consideration of the similarity law, to clarify the mechanisms involved, focusing on
the linear and nonlinear seismic responses of the tower and cables.
Key Words : long-period seismic excitation, long-period structure, PC cable-stayed bridge, seismic response analysis, shaking table test

structure because their resonant frequencies matchthe dominant frequencies of the ground motion, thedamage to infrastructure caused by far-field earthquakes has been investigated more extensively. The
reason for this is that large far-field earthquakes
have occurred in recent years, such as the 2003 Tokachi-oki earthquake and the 2004 SumatraAndaman earthquake. In the Tokachi-oki earthquake,a terrible fire occurred at an oil tank located on the
Tomakomai Plain due to sloshing of its contents
resulting from the long-period seismic excitation.
The source of the Sumatra-Andaman earthquake isestimated to be a region about 1000 km wide from

1. INTRODUCTION
The infrastructure sustaining our socio-economic
activity has been affected by recent severe earthquakes. These earthquakes are classified dependingon the two distinct event mechanisms involved:
plate boundary and inner slab earthquakes (far-field
earthquakes), and active fault earthquakes (nearfield earthquakes). The former excite long-period
and long-duration ground motion, and the latter excite ground motion that contains strong, shortduration impulse components. Although both typesof earthquakes cause devastating damage to infra-

982

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

north to south, with a fault length of about 560 km,
a fault width of about 150 km, and a maximum dislocation of about 13.9 m. In addition to these previous far-field earthquakes, the possibility of a Tokai,
Toh-Nankai, or Nankai Earthquake in the next 30
years is considered to be very high. Since far-field
earthquakes excite long-period and long-duration
ground motion, long-period structures subjected totheir seismic excitation might be severely damaged.
In terms of the definition of the range of the ‘longperiod’ and ‘long-duration’, it has been establishedfrom the field of strong motion seismology that thefundamental period of a ground motion reaches tomore than about 2.0 sec or 2.5 sec and the longperiod components contain dominantly in the
ground motion, and in addition the duration of themain and subsequent excitation becomes more thanseveral minutes that correspond to more than 3.0
minutes or 4.0 minutes.1)
On the other hand, large active-fault earthquakes,
such as the 1999 Chi-Chi, Taiwan earthquake, excite long-period components from 1.0 sec to 2.0 sec
due to the large rupture of the fault. In this earthquake, strong ground motion was observed due tothe rupture of the Chelungph Fault, which is about
80 km wide from north to south and about 40 km
wide from east to west; in fact, ground surface
movement of several meters occurred along the fault.
A large cable-stayed bridge constructed ofprestressed concrete girders (PC cable-stayed
bridge) located about 6 km from the epicenter wasdamaged by the seismic excitation; for example, thecover concrete of the longitudinal reinforcements on
its tower bottom spalled off.2), 3), 4) This was an important opportunity to analyze the bridge in order tounderstand the damage mechanisms of long-period
structures when subjected to long-period components of a ground motion, because there are few recorded historical incidents of this type.
Many researchers are involved in computer-based
simulations to predict long-period ground motion
due to a large far-field earthquake. Kamae et al.,5)for instance, carried out a simulation of the groundmotion that would be excited in the Osaka Plain due
to the anticipated Nankai earthquake using the finite
differential method. The simulation of long-period
ground motion with a period of more than 2.0 sec or
2.5 sec agreed well with observatory records; therefore, these simulated ground motions may be useful
as input ground motions in conducting seismic response analyses of long-period structures.
The seismic damage of a structure subjected tothis simulated ground motion could be assessed because the finite differential method simulates the983

effects of 1) the rupture process, 2) the undergroundstructure, and 3) the ground surface. Otsuka et al.6)
evaluated long-period ground motion at the site of aplanned long-span bridge structure in Tokyo Bay byadopting the same method as described above. Komori et al.7) clarified the effectiveness of strengthening the structural components of large bridges in the
Metropolitan Expressway by using their own simulated long-period ground motion.
Many researchers are involved in theoretical andnumerical simulations to understand the mechanisms associated with the seismic response of cablestayed bridges. For instance, Nazmy and AbdelGhaffar 8),9) developed a theoretical evaluation
model of the seismic response of large cable-stayed
bridges, and they conducted numerical studies basedon their theory.
In contrast to these theoretical and numericalstudies, however, the seismic responses of cablestayed bridges have not been sufficiently studied
experimentally. Vilaverde and Martin10) carried out
seismic shaking table tests on models to evaluate theeffectiveness of seismic control devices for cablestayed bridges. Kawashima et al.11) evaluated thedamping mechanism of cable-stayed bridges in experimental studies using 1/150-scale models. Kitazawa et al.12) investigated the effectiveness of dampers installed on the Higashi-Kobe Bridge by shaking
table tests.
Despite the abundance of data from these studies,
the mechanisms involved in the seismic response ofcable-stayed long-period bridges when subjected toa long-period component of ground motion have notyet been sufficiently clarified from theoretical andexperimental points of view. Especially, no experimental studies to clarify the seismic response of acable-stayed bridge when subjected to a long-period
ground motion by considering the similarity ratiosof a bridge model with a prototype cable-stayed
bridge, have ever tried.
In view of the above, in this study the mechanisms associated with the seismic response of a PC
cable-stayed bridge when subjected to a long-period
ground motion were clarified by conducting seismic
response analyses and shaking table tests considering the similarity law. This study defined the ‘longperiod’ of a ground excitation as the period of morethan 2.0 sec or 2.5 sec referring the previous definition. The natural period of the subject long-period
structures was from 2.0 sec to 3.0 sec. The longperiod components of the simulated ground motionin the 1999 Chi-Chi, Taiwan earthquake and thesimulated long-period ground motions in the anticipated Nankai earthquake were used as the input gro-

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
120m

120m
S

N

Pullout of the cable at the anchorage

58m

Spalling-off of the cover concrete at the bottomof the tower
Buckling of the longitudinal reinforcements

Pullout of many sockets

Damage of the end of the main girder
Damage of the pier beam

Damage of the end of the main girder
Damage of the pier beam
Cable No; No.1 to No.17

SouthboundSpalling-off of the cover concrete at the rigid
connection between the tower and the girder

NorthboundSpalling-off of the cover concrete at the rigid
connection between the tower and the girder
Cracks at the bottom of the pier on its east
and west side faces

Fig. 1 Damage to the Ji-Lu Bridge. 4)

the epicenter of the 1999 Chi-Chi, Taiwan earthquake. Its longitudinal direction is from north tosouth. Table 1 shows its structural characteristics.
The tower and the pier are constructed of reinforced
concrete (RC) columns and the sectional area of thetower is 4.0 m × 3.0 m at the top, increasing to 6.0
m × 3.0 m at the bottom. The area ratio ρ l of thelongitudinal reinforcements and the volume ratio ρ sof the hoop reinforcements are respectively 2.88%
and 4.73% at the top of the tower, and 2.94% and14.17% at the bottom of the tower. The cross section of the pier is elliptic and its sectional area is 6.0
m × 6.3 m. The area ratio ρ l of the longitudinal reinforcements and the volume ratio ρ s of the hoop
reinforcements of the pier are 1.10% and 1.89%,
respectively. The bridge cables are of the 2-plain
type and the total number of cables is 68. Table 2
shows the tension strengths of the cables. The cable
numbers indicated in Table 2 correspond to thoseindicated in Fig. 1 described below.
4)Fig. 1 shows the damage to the Ji-Lu Bridge.
The bridge was under construction during the eventand four precast panels near the rigid connection
between the tower and the deck were not yet built.
The cover concrete on the east and west sides at thebottom of the tower spalled off and the longitudinal
reinforcements were buckled. Shear cracks occurredin the beams of the piers because the deck moved in
the transverse direction. The reason for this damageis that the bridge was subjected to strong groundmotion in the transverse direction, namely, from east
to west. Moreover, the deck concrete at the joint
section between the deck and the tower spalled off,and local buckling of the longitudinal bars in thedeck occurred at the south part of the joint section.
The diagonal cables at the anchorage section were
pulled out.
Kosa et al.3) and Tai and Liou13) analyzed the vibrational modes of the bridge, as shown in Table 3.
The first mode is predominant in the transverse direction from east to west, the second mode is theanti-symmetric longitudinal vibration from north toTable 1 Structural characteristics of the Ji-Lu Bridge.
Structural typeTwo-spanned PC cable-stayed bridge

Total length / span

240 m / 120 m

Height of tower

58 m

Tower

Hollow type RC

PierRC, elliptic section of 6.0 m×6.3 m

Foundation

Pile foundation

Table 2 Tensions of cables.
Cable No.

Tension (MN)

Cable No.

Tension (MN)

1

7.54

10

5.72

2

6.15

11

5.84

3

5.33

12

6.54

4

5.06

13

6.05

5

5.06

14

6.28

6

5.15

15

6.54

7

5.30

16

6.53

8

5.44

17

5.51

9

5.58

und motions in the numerical analyses and the shaking table tests. First, we analyzed the seismic damage to the Ji-Lu Bridge in the 1999 Chi-Chi, Taiwan
earthquake using the simulated long-period groundmotions, and second, the mechanisms associatedwith the seismic response of a PC cable-stayed
bridge when subjected to the simulated long-period
ground motions in the 1999 Chi-Chi, Taiwan earthquake and the anticipated Nankai earthquake, wereclarified by conducting shaking table tests.

2. SIMULATION OF INPUT GROUNDMOTION AT THE SITE OF THE JILU BRIDGE DUE TO THE 1999 CHICHI, TAIWAN EARTHQUAKE(1) Ji-Lu bridge and its seismic damage
The subject bridge is the Ji-Lu Bridge, a two-span
PC cable-stayed bridge located about 6 km S30W of984

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Table 3 Natural periods of the Ji-Lu Bridge. 3),13)
Mode No.

Natural period, fromreference 3 (sec)Natural period, fromreference 13 (sec)

1

1.99

2.28

2

1.66

1.80

3

1.19

1.05

4

1.08

1.03

epicenter★ Hypocenter

N003E

★

25km
80km

PlainsFoothills

Mountains

40km

TCU13674.5km119km

Fig. 3 Fault source model.14)

TCU051
TCU072
TCU063
TCU071
TCU074
TCU089TCU120

epicenter ★
Ji-Lu Bridge

K

Depth（m）
0
200
800
1500
2000
3000
3700
8000
13000
17000
25000
30000
35000
50000
55000

TCU079TCU078

CHY074

Fig. 2 The analysis region.

south, the third mode is the vertical vibration, andthe fourth mode is the sway mode in the longitudinal direction from north to south.

Plains123456Foothills
200
8
910
9
1910
10
11
12

Mountains
7
13
2000
4000
9000

17
18
19
20
21
22

14
15
16

Fig. 4 Underground structure model (modified the results fromreferences 14, 15).

(2) Simulation of input ground motion at the siteof the Ji-Lu bridge
In this section we simulate the seismic ground excitation at the site of the Ji-Lu Bridge, which is usedas the input ground motion when conducting theseismic dynamic analyses and the shaking table
tests. Because the ground excitation at the site of the
Ji-Lu Bridge was not recorded during the 1999 ChiChi, Taiwan earthquake, the dependence of thelong-period components of the simulated groundexcitation with the damage to the bridge can be obtained by doing seismic dynamic analyses with thesimulated ground excitation as the input ground motion for the Ji-Lu Bridge. As well as in the seismic
response analyses, in the shaking table tests, thesimulated ground excitations of the anticipatedNankai earthquake, computed by Kamae et al.,5) areused. They adopted hybrid method to simulate both
short-period components and long-period ones ofthe subject ground motion, then we used long-period
components of the simulated ground excitations of
the anticipated Nankai earthquake.
a) Analysis region
The 1999 Chi-Chi, Taiwan, Earthquake of M w =7.6 occurred on September 21, 1999, with its epicenter in the town of Chi-Chi, Taiwan. The Chelungph Fault ruptured for about 80 km from north tosouth, resulting in severe ground dislocation.14)
From the rupture size of the Chelungph Fault, we set
an analysis region 119 km wide from north to southand 74.5 km wide from east to west in theplain, as shown in Fig. 2. The locations of the epicenter, the subject bridge, and the observatory stations are shown in Fig. 2.
b) Source model
The fault source model derived by Sekiguchi and
Iwata14) was used, as shown in Fig. 3. From theirmodel the fault sources were 80 km wide from northto south, 40 km wide from east to west, and 25 km
deep. The rupture surface of the fault was classified
into 26 × 13 subfaults, and then each subfault wasmodeled as a point source. The rupture process ofeach point source was modeled as eight time windows. The width of each window was 2 sec, and thephase difference between two successive windows
was 1.2 sec. The derivative of the smoothed rampfunction was used for the source time function.
c) Underground structure
Chung and Yeh15) evaluated the velocity structurein the region from 22.7 to 23.7 degrees north latitude and from 120.0 to 121.0 degrees east longitude
using a dispersion analysis. The subject underground structure in the region shown in Fig. 2 wasassumed to be the same as the above structure usedby Chung and Yeh. Fig. 4 and Table 4 show theunderground structure in the section from east to
west. The boundary lines between the mountains
and the foothills and between the foothills and theplains were determined based on topographicalmaps of the region.16) The surface structure in theplains down to 200 m beneath the surface was estimated as shown in Table 4 from the velocity struc-985

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Table 4 Parameters of the velocity structure (modified the results from references 14, 15).
Vp (m/s)

Vs
(m/s)

1

1000

500

1600

90

2

1980

900

2100

100

3

2900

1320

2200

100

4

3476

1580

2300

150

5

3484

1960

2400

200

6

4551

2560

2500

250

7

2000

1000

1900

90

8

2880

1550

2000

100

9

3150

1700

2050

200

10

4370

2500

2300

250

11

5130

2850

2400

250

12

5900

3300

2600

270

13

3480

1960

2400

200

14

4480

2620

2500

250

15

5250

3030

2600

250

16

5830

3350

2650

270

17

6210

3610

2700

300

18

6410

3710

2750

350

19

6830

3950

2800

400

20

7290

4210

3000

500

21

7770

4490

3100

500

22

8050

4680

3100

500

Layer No.

Mass density (kg/m3)

119km
Absorbing boundary

12km

Q (Hz)

Region 1：24km
Mesh size
200m×200m×100m
Region 2：31km
Mesh size
600m×600m×300m

Fig. 5 Spatial region for simulation.

sec.
To guarantee numerical stability in the explicit
approximation of the wave equation, it is necessary
to restrict the wavefront propagation in a unit time
step Δt to a unit grid. For grid distance h, the necessary condition for numerical stability in the finite
differential scheme is:20)
Δt < 0.495

Table 5 Numerical conditions.
Conditions

ValuesRegion 1

Upper frequency limit

0.5 Hz
12000

Time integration

0.005 sec

Time duration

Mesh size
Depth at the boundary between
region 1 and region 2
No. of mesh grids of absorbing
boundary
Damping ratio of absorbing
boundary

60 secHorizontal
200 m

Horizontal
600 m

Depth
100 m

Depth
300 m
24 km

60

20

0.005

0.015

h
V max

(1)

where Vmax is the maximum wave velocity. For thereason described above, the time step Δt was set to0.005 sec and the time duration to be simulated was
set to 60 sec shown in Table 5.
Levander21) indicated that a grid distance h of lessthan one-fifth of the simulated wave length is required in the fourth-order approximation of the finite differential scheme. It has also been shown thatthe numerical damping and dispersion become
stronger when the analyzed wave length becomesmuch shorter than one-fifth.22), 23) As shown in Table 4, the S wave length in layer 1 was a minimumof 500 m ( VS =500m/s). In addition, considering thefrequency limit of 0.5 Hz, the analyzed wave length
was 1000 m. Hence, the grid distances in the region
1 in the x direction and the y direction, that are
horizontal directions, were the same, namely 200 m.
The grid distance in the region 1 in the z direction,that is vertical direction, was set to 100 m. The reason for this is that the numerical accuracy isstrongly dependent upon the mesh size in the z direction. The discrepancy of the phase between thesimulated waveforms and the observed waveforms
became larger when the mesh size in the z direction
was set to 200 m compared to when it was set to 100m.
In the Aoi and Fujiwara method, discontinuous
mesh grids are defined to reduce the CPU memory
required for the simulation. As shown in Fig. 5, region 1, in which the grid size is set to be smaller, issuitable for the complex surface structure and region
2, in which the grid size is set to be larger, is suit-

Region 2

No. of sample points

74.5km12km

ture obtained from the microwave survey by Tokimatsu and Sekiguchi.17)d) Numerical algorithm: finite differential
methodAmong the numerous finite differential algorithms available, in this study we adopted the one
proposed by Aoi and Fujiwara,18),19) which is afourth-order approximation for the spatial derivative
and a second-order one for the time derivative withdiscontinuous grids.
The spatial region simulated was 119 km widefrom north to south, 74.5 km wide from east to west,
and 55 km deep, including the absorbing boundary.
Table 5 shows the parameters used in the numericalsimulation. The frequency limit was set to 0.5 Hz
because we are concerned only with long-period
components of seismic excitations of more than 2.0

986

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

EW
CHY074（Foothills）

TCU078（Foothills）

Maximum analyzed velocity (m/s)
0.141

NS
0.098

0.220

0.135

0.197

0.170

0.155

0.137

0.110

0.159

0.125

0.098

0.175

0.277

0.172

0.199

0.224

0.124

TCU072（Foothills）

TCU074（Mountains）

TCU063（Plains）

TCU051（Plains）

0.161

0.530

0.356

0.312

0.498

0.449

0.484

0.350

0.386

0.284

0.421

0.192

0.148

0.124

0.322

0.182

0.194

0.691

0.310

0.377

0.412

0.409

0.637

0.238

0.724

1.609

1.254

0.463

0.636

0.842

0.619

0.845

0.872

0.326

1.042

1.064

0.939

0.625
TCU120（Plains）

0.101
0.098

0.159

TCU071（Foothills）

Calculated waveform
Observed waveform

0.135

0.190
Maximum observed velocity (m/s)

TCU079（Foothills）

TCU089（Foothills）

UD

0.645

0.245

0.305

0.305

0.692

TCU136（Plains）

Fig.6 Comparison of the simulated waveforms with the observatory records.

able for the deeper underground structure. The gridsize in region 2 was set to be 3 times larger than thatin region 1. Since the depth of the fault source wasabout 24 km beneath the ground surface, the depthof the discontinuous surface between region 1 andregion 2 was set to be 24 km beneath the groundsurface. The absorbing boundary was based on the
one proposed by Cerjan et al.24) and the nonreflection one proposed by Clayton and Engquist.25)
The number of mesh grids and the damping ratios of
the absorbing boundary were set by referring to thenumerical study of Aoi and Fujiwara19), as shown in
Table 5.

(3) Simulation of the seismic excitationa) Comparison of the simulated waveforms withthe observatory records
The simulated waveforms were compared withthe observatory records of the Central Weather Bureau (CWB),26) as shown in Fig. 6. Eleven records
were used in the comparison. All simulated and observed waveforms were filtered by a band-pass filter
from 2.0 sec to 20.0 sec.14), 27) The seven simulated
waveforms at observatory stations CHY074,
TCU078, TCU079, TCU089, TCU071, TCU072,
and TCU074 agreed well with the observed records
in terms of the accuracy of the amplitude and phaseof the waveforms. To prove the agreement, the Fourier transforms of above seven simulated waveforms
and the corresponding observed ones to the frequency domain were performed. The agreement as-987

Velocity (m/s)

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

0.5

Simulated waveform at the site of Ji-Lu Bridge
Simulated waveform at station TCU078

EW

Tower: Nonlinear beam element

0-0.5

Cable: Truss element

0

10

20

30

Time (sec)

40

50

60

Girder: Linear beam element

Velocity (m/s)(a) EW component
0.5

NSFig. 9 3D frame model of the Ji-Lu Bridge.

0

-0.5

0

10

20

30

Time (sec)

40

50

60

50

60

the central and south parts, and also to the fact thatthe fault rupture in the north part was skewed. The
third reason is related to the upper limit of the wave
length in the plain, which was smaller than that in
the foothills and the mountains.
b) Simulation of the ground excitation at the siteof the Ji-Lu bridge
The accuracy of the simulated ground excitationin the foothills and the mountains was verified from
Fig. 6. We simulated the ground excitation at thesite of the Ji-Lu Bridge, which is located in thefoothills. Fig. 7 shows a comparison of the simulated ground excitation at the site of the Ji-Lu
Bridge with the simulated one at station TCU078,
which is located about 7.5 km from the bridge andin the foothills. Fig. 8 shows their velocity response
spectra with a damping ratio of 0.05.
From Fig. 7, the amplitudes and phases were
found to differ between the simulated waveforms at
the site of the Ji-Lu Bridge and those at station
TCU078, and from Fig. 8, the velocity response
based on those waveforms also to differ by factorsof two to three in the period from 2.0 sec to 7.0 sec.
The reason for above difference is that the distanceof the bridge and the station TCU078 is about 7.5km
and the wave propagation depending on the fault
rupture process based on the Fig. 3 differs between
the two sites.

(b) NS component
Velocity (m/s)

Connection between tower and girder:
Rigid element
Pier: Nonlinear beam element

0.5

UD

0

-0.5

0

10

20

30

Time (sec)40(c) UD component
Fig. 7 Comparison between the simulated waveforms at the siteof the Ji-Lu Bridge and those at station TCU078.
NS comp. at Ji-Lu Br.
EW comp. at Ji-Lu Br.
UD comp. at Ji-Lu Br.
NS comp. at TCU078 st.
EW comp. at TCU078 st.
UD comp. at TCU078 st.

Velocity response spectrum (m/s)

1.5

1.0

0.5

0
0

5

10

15

20

Period （sec）

Fig. 8 Comparison of the velocity response spectra with adamping ratio of 0.05 between the simulated waveforms at the site of the Ji-Lu Bridge and those at station
TCU078.

sociated with the shape and trend of the Fourier amplitude spectra and the Fourier phase spectra obtained from the simulated waveforms and thosefrom the observed ones was confirmed. These stations are located in the central part and the southpart of the simulated region, on the foothills and themountains. In contrast, the four simulated waveforms at stations TCU120, TCU063, TCU051, andTCU136 disagreed with the observed records interms of the accuracy of the phase. These stations
are located in the north part of the simulated region,on the plains. We hypothesize three main reasonsfor these results: the values of the S wave velocity
and the P wave velocity in the plains were not reasonable; the source model in the north part of thesimulated spatial region was not accurate and thegrid size in the surface structure in the plain waslarge. The second reason is related to the fault rupture in the north part, which was larger than that in

3. PRELIMINARY SEISMIC RESPONSEANALYSIS OF THE JI-LU BRIDGEBEFORE SHAKING TABLE TESTS(1) Model of the Ji-Lu bridge
The seismic response of the Ji-Lu Bridge whensubjected to the simulated seismic excitation derived
in the previous section was analyzed. The bridge
was modeled by the 3 dimensional (3D) frame
model shown in Fig. 9. Nonlinear beam elements
were adopted to model the tower and the pier, andthe moment-versus-curvature relationship was assumed to be the idealized Takeda hysteresis
model.28) The values of the moment and the curvature at the crack, the yielding, and the ultimate
points were determined by referring to the research988

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12(a) 1st mode(b) 2nd mode(c) 3rd mode(d) 4th mode
Fig. 10 Mode shapes of the numerical model of the Ji-Lu Bridge.

of Abe.29) The ratio of the unloading stiffness to theinitial stiffness was assumed to be 0.4. Because thesectional area of the tower varied gradually from the
top to the bottom, the section of the tower was modeled by three idealized sections at the top, middle,
and bottom.
A linear beam element was used to model themain girder, and truss elements having only tension
stiffness were used to model the cables. The joint
connection between the tower and the main girder
was modeled by a rigid element. The mass of eachcable was divided into the mass at the end connectedto the tower and the mass at the other end connectedto the main girder. The values of the modulus ofelasticity, the moment of inertia, and the torsion
constants of the pier, the main girder, and the cables
were determined by referring to the results of Tasaki
et al.4) The motion of the foundation was idealized
by using a model including a sway spring, a rotation
spring, and their coupled spring elements.
The longitudinal displacement and the momentwith respect to the transverse axis at both ends ofthe main girder were free, and the others were fixed.
The idealized damping matrix in the equation of
motion was obtained using the Rayleigh damping
matrix. The constants in the summation of mass matrix and stiffness matrix were defined using the frequencies in the 1st and 8th modes, in which modal
damping ratios are assumed to be the same of 0.02.
Table 6 and Fig. 10 show the natural periods andmode shapes of the numerical model of the bridge
obtained from the modal analysis. The first and second modal periods (symmetry transverse mode andanti-symmetry longitudinal mode) shown in Table 6
are more similar to those with the model derived by

Table 6 Natural periods and mode shapes of the numericalmodel of the Ji-Lu Bridge.
Mode No.

Natural period (sec)Mode shape

1

2.005

Symmetry, TR dir.

2

1.447

Anti-symmetry, LG dir.

3

0.637

Symmetry, UD dir.

4

0.573

Anti-symmetry, LG dir.

5

0.400

Symmetry, TR dir.

6

0.373

Anti-symmetry, LG dir.

7

0.361

Symmetry, UD dir.

8

0.230

Anti-symmetry, LG dir.

9

0.217

Symmetry, UD dir.

0.157

Anti-symmetry, LG dir.

10

(TR: Transverse, LG: Longitudinal, UD:Vertical)

Kosa et al.3) than those with the model derived by
Tai and Liou13) (refer Table 3). The third and fourthmodal shapes (symmetry vertical mode and antisymmetry longitudinal mode) show close correspondence between our model and the models by
Kosa et al., and Tai and Liou, but there are the differences between those modal periods shown in Table 6 and those by Kosa et al., and Tai and Liou,that become about 0.4 sec. The reason of this is thatin our model, previously mentioned, the section of
the tower was modeled by three idealized sections at
the top, middle, and bottom under the structural
condition with the sectional area of the tower varied
from the top to the bottom.
(2) Seismic damage assessment of the Ji-Lu
BridgeThe displacement and the acceleration at the top of

989

0.4

Displacement (m)Acceleration (G)Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

0.2
0
-0.2
-0.4

Ji-Lu Bridge
0

20

40

60
80
Time (sec)

100

120
Displacement (m)Acceleration (G)

0.4
0.2
0
-0.2
-0.4

TCU078
0

20

40

60
Time (sec)

80

100

120

0.4
0.2
0
-0.2
-0.4

Ji-Lu Bridge
0

20

40

60
Time (sec)

80

100

120

0.4
0.2
0
-0.2
-0.4

TCU078
0

20

40

60
Time (sec)

80

100

120

(a) Acceleration response(b) Displacement response
Fig. 11 Acceleration and displacement responses at the top of the tower in the transverse direction when subjected to the simulated
excitation at the site of the Ji-Lu Bridge and that at station TCU078.
200

the seismic responses when subjected to the simulated excitation at the site of the Ji-Lu Bridge andthat at station TCU078 were almost the same aroundthe period of 2.005 sec.

Yielding

150
Moment (MNm)

100

Cracking

50
0

4. SHAKING TABLE TESTS

-50
-100
-150
-200

(1) Bridge model and experimental setupa) Design of the bridge model
To clarify the mechanisms associated with theseismic response of a PC cable-stayed bridge whensubjected to a long-period seismic excitation, we
selected a typical PC cable-stayed bridge with anatural period from 2.0 sec to 3.0 sec, such as the JiLu Bridge shown in the previous sections, as themodel bridge for the series of shaking table tests.
We considered the following three requirements forthe design of the bridge model:
i. The similarity ratio of acceleration should be
set to 1.0 because it is difficult to control gravitational acceleration in the experiments.
ii. The bridge model should be simple in terms of
its fabrication and construction.
iii. The model should be as large as possible toeliminate the effects of irregularity in its configuration and variations in the properties of thematerials used to build the bridge model.
Based on these requirements, the similarity ratiosof the model with respect to the prototype bridge
were determined as shown in Table 7. The similarity ratio of the length was set to 100 by considering
the size of the shaking table and the ease of constructing the model, and the similarity ratio of thetime was 10.
b) Details of the bridge model
As shown in Figs. 13 and 14, the total length ofthe main girder was 2400 mm, and the height of thetower was 1000 mm. Poly-vinyl-alcohol (PVA)

TCU078Ji-Lu Bridge
-1

-0.5
0
0.5
-3
Curvature ( x 10 1/m)

1Fig. 12 Moment-versus-curvature relationship when subjectedto the simulated excitation at the site of the Ji-Lu
Bridge and that at station TCU078.

the tower in the transverse direction were computed
as shown in Fig. 11 when the bridge was subjectedto the simulated seismic excitation at the site of thebridge and that at station TCU078. Fig. 12 shows
the moment-versus-curvature relationship at the bottom of the tower. Fig. 12 indicates that damage beyond the crack level occurred at the bottom of thetower when subjected to both excitations. However,yielding-level damage did not occur at the bottom of
the tower, although yielding of the longitudinal reinforcements and spalling-off of the cover concrete
actually occurred in the Ji-Lu Bridge. In addition,
despite the difference between the simulated excitation at the site of the Ji-Lu Bridge and that at station
TCU078, as shown in Figs. 7 and 8, the momentversus-curvature relationships for those cases did
not differ. The reason for this is that there is a slightdifference of the velocity response spectra at theperiod of 2.005 sec, which is the 1st natural periodof the bridge, as shown in the site of the Ji-Lu
Bridge contained more long-period components beyond 2.0 sec than that at station TCU078. Hence,990

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Table 7 Similarity ratios.
Dimension

lt −2
l
t
ρ
t −1
lt −1
ρl 3
ρl 4 t −2
ρl 4 t −2
ρl 3 t − 2l2l4
ρl 2 t −2
ρl 6 t −2
ρl 4 t −2
ρl 3 t − 2
ρl 5t −2Compression
Secantmodulus ofelasticity Ec
(GPa)
15.5

Maximum
strength σc
(MPa)
33.3

TensionStrain at
maximum
strength εc (%)

Stress at initial
cracking σc(MPa)

Ultimate strain
εu (%)

0.46

3.52

1.00

30mm
5mm
30mm
Diameter of
0.9mm

Fig. 15 Cross section of the tower model.
0.06
0.05
Moment （kNm）

Acceleration
LengthTime
Density of massFrequency
Velocity
Mass
Force
WeightWeight per unit length
Area
Moment of inertia
Modulus of elasticity
Flexural rigidity
Tensile rigidity
Spring coefficient in sway
Spring coefficient in rocking

Table 8 Mechanical properties of the PVA concrete.
Similarity ratio
1
100
10
1
0.1
10
1000000
1000000
1000000
10000
10000
100000000
100
10000000000
1000000
10000
100000000

0.04
0.03
0.02
0.01
0
0

Fig.13 Cable-stayed bridge model.
Supplemented
mass of 9.96kg

100

200
300
400
Curvature (×10-6/mm)

500

600

Fig. 16 Moment-versus-curvature relationship at the bottom of
the tower model.

Accelerometers and laser displacement
sensors

The resulting cross-section of the tower is shown in
Fig. 15. Its sectional area was 30 mm × 30 mm, andSupplemented massfour longitudinal reinforcements 0.9 mm in diameterof cable
Calibrated strain with tension strengths of 336 MPa were used. The
gages to measure
Cable 4 Cable 3 Cable 2 Cable 1 tension strength
skeleton of the moment-versus-curvature hysteresisat the bottom of the tower was numerically obtained
Supplemented mass of 3.0kg×8
Main girder: Steel plate2400mmby modeling the tension stress resulting from theFig.14 Details of cable-stayed bridge model.
PVA fibers based on the constitutive laws of Shimizu et al.31), as shown in Fig. 16. It seems reasonconcrete was used as the concrete for the tower. Beable to suppose that the cyclic behavior associatedcause the sectional area of the tower was small (30with the stress-versus-strain relationship of the used
mm × 30mm), as described below, and the hoop rePVA concrete has similar trend as that from the reinforcements could not be used to constrain the coresearch of Billington and Kesner32), however it needs
concrete, the PVA concrete was used to effectively
further consideration in this study since we could
constrain the core concrete due to the tension stressnot obtain the cyclic behaviour of the tower model
provided by fibers in the PVA concrete. The values
experimentally. Brass weights of 9.96 kg were atof the sectional area and the sizes of the longitudinaltached at the top of the tower model, as shown inreinforcements of the tower were determined by reFig. 14, to satisfy the similarity ratio with respect toferring to the study of fiber-strengthening concrete
the mass of the tower.
columns of Sakai et al.30) The content of the PVA
Although the girders of the actual bridge (protofibers in the concrete was 2% by volume. Table 8
type bridge) were formed of prestressed concrete,shows the mechanical properties of the PVA confor the sake of ease of manufacturing, the girders ofcrete used for the tower model.
the model were steel plates of 50 mm in width and 6
The height and the sectional area of the tower
mm in height to satisfy the similarity ratio with recross-section, and the sizes of the longitudinal reinspect to the flexural rigidity. Eight brass weights offorcements were determined to satisfy the similarity
each 3.0 kg were attached to the girders to satisfy
ratios with respect to length and flexural rigidity.
the similarity ratio with respect to the mass of theTower: PVA concrete

1000mmFree of displacement in
the longitudinal direction
and free of moment in thetransverse direction at
both ends of the main
girder
Cable 8 Cable 7 Cable 6 Cable 5

Cable: Twist steel wire991

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Table 10 Natural periods and damping ratios of the bridge
model before and after the shaking table tests.

Table 9 Prestressed tension strength of cables.
Cable No.
1
2
3
4
5
6
7
8

Tension (N)
43.7
34.6
32.5
44.7
44.7
32.5
34.6
43.7

girders.
Idealized cables were designed based on the similarity ratio with respect to the force by referring to
the tension strength at a permanent strain of 2%;
thus, twisted steel wires 1.5 mm in diameter with atension strength of 269.5 N at a permanent strain of
2% were used for the model cables. In the prototype
bridge, the 68 cables are tensioned in parallel at thecenter line of the girder in the longitudinal direction,then the 34 cables should be idealized in the tests.
However the number of cables was reduced fromthe 34 cables to the 8 ones. The reason for this isthat it is quite difficult to perfectly satisfy the similarity ratio for all 34 cables from the viewpoint of
the construction of the cable models and theprestressing of the tension strength of the cables.
In spite of the reduction of the number of the cables, to satisfy the similarity associated with theprestressed strength of the cables between the prototype bridge and the model, and asscociated with themoment acting onto the section of the girder withrespect to the transverse axis due to the cable tension, the prestressed tension strength of each modelcable and its attachment positions to the girder andthe tower were determined so that the vertical component of the tension for each cable was the same as
the sum of the vertical components of the tensions
for the cables provided before reducing the numberof cables to 8, and so that the resulting moment on
the girder from the tension of each cable was thesame as the sum of the moments on the girder fromthe tensions of the cables provided before reducing
the number of cables to 8. Table 9 shows theprestressed tension strength of the cables. The cable
numbers in Table 9 correspond to those in Fig. 14.
The values of the prestressed tension strength inTable 9 are the required ones before the start of theshaking table test. However, because of the difficulty of prestressing the tension for 8 cables, theerror of the prestressed tension strength with respect
to the required values shown in Table 9 varied from
0.1% to 6.4%.
This experiment was focused on clarifying theseismic response of the tower and cables. Hence,the pier was idealized by a rigid body made of acircular steel bar 30 mm in diameter. The free andTest No.

Natural period
before the test (sec)Damping ratio
before the test

Natural period
after the test (sec)

1

0.318

0.00604

0.318

2

0.313

0.00678

0.315

3

0.314

0.00877

0.353

4

0.322

0.00858

0.325

5

0.325

0.00803

0.355

6

0.311

0.00949

0.312

7

0.312

0.00992

0.345

8

0.345

0.023

0.426

9

0.316

0.00688

0.316

10

0.316

0.00594

0.316

11

0.316

0.00676

0.315

12

0.315

0.00686

0.320

13

0.318

0.00638

0.318

14

0.314

0.00877

0.353

15

0.318

0.00769

0.338

16

0.320

0.00835

0.320

17

0.320

0.00841

0.327

the fixed support conditions of the longitudinal, thetransverse, and the rotational movements at bothends of the girder were idealized by combining aslider and a bearing.
Acceleration in the tower top and at the towerbottom in the transverse and longitudinal directions
is recorded by accelerometers and displacement in
the same positions as acceleration is recorded bylaser displacement sensors, as shown in Fig. 14.
Tension strength of cables is measured by the strain
gage attached on the edge of each cable, whose
value is related with tension strength before the tests.
Sampling frequency at which all data above are recorded is 1000 Hz.
The average values of the dominant natural period
and the damping ratio with respect to the transverse
direction of the bridge model were computed basedon the displacement waveforms at the top of thetower obtained from the free vibration tests. Three
free vibration tests were conducted before and after
each test. Table 10 shows the computed natural periods before and after the tests and the computed
damping ratios before the tests. These natural periods for the bridge model correspond to a natural
period of more than 3.0 sec for the actual bridge
based on the similarity ratio with respect to timeshown in Table 7.
The natural period with respect to the longitudinal
direction of the bridge model was evaluated by the
Fourier transforms of the acceleration waveforms
obtained from the free vibration tests. The results
indicate that there were several predominant coupled modes in the period ranging from 0.1 sec to0.31 sec.
(2) Input ground motion for the shaking table
test
Table 11 shows the test cases for the shaking ta-

992

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12of about 0.3 sec, which is nearly equal to the dominant period of the bridge model as shown in Table
10, are larger than those at other periods. On theother hand, the displacement responses at the natural
period of about 0.3 sec do not become larger thanthose at other periods.

Table 11 Shaking table tests.
Test
No.

Directionof shaking

Input excitation
Simulated waveform at Ji-Lu
Bridge in the 1999 Chi-Chi,
Taiwan EQ.
Simulated waveform at Ji-Lu
Bridge in the 1999 Chi-Chi,
Taiwan EQ.
Simulated waveform at Ji-Lu
Bridge in the 1999 Chi-Chi,
Taiwan EQ.
Simulated waveform at OSK008
in the anticipated Nankai EQ.

1

2

3
4

Component.

Amplification
factor of
amplitude

EW

1

EW

2

EW

3

EW

1

5

Simulated waveform at OSK008
in the anticipated Nankai EQ.

EW

2

6

Simulated waveform at OSK008
in the anticipated Nankai EQ.

NS

1

7

Simulated waveform at OSK008
in the anticipated Nankai EQ.

NS

2

8

Simulated waveform at OSK008
in the anticipated Nankai EQ.

NS

3

9

Simulated waveform at OSK003
in the anticipated Nankai EQ.

EW

1

10

Simulated waveform at OSK003
in the anticipated Nankai EQ.

NS

1

11

Simulated waveform at OSK005
in the anticipated Nankai EQ.

EW

1

NS

1

NS+EW

1

NS+EW

2

TR

12
13

14
15

TR+LG

Simulated waveform at OSK005
in the anticipated Nankai EQ.
Simulated waveform at Ji-Lu
Bridge in the 1999 Chi-Chi,
Taiwan EQ.
Simulated waveform at Ji-Lu
Bridge in the 1999 Chi-Chi,
Taiwan EQ.
Simulated waveform at OSK008
in the anticipated Nankai EQ.

NS+EW

1

16

Simulated waveform at OSK003
in the anticipated Nankai EQ.

NS+EW

1

17

Simulated waveform at OSK005
in the anticipated Nankai EQ.

NS+EW

1

5. MECHANISM OF THE SEISMIC RESPONSE OF THE BRIDGE MODEL(1) Linear seismic response of the bridge model
when subjected to the uni-lateral shaking
Fig. 19 shows the maximum acceleration and displacement responses in the transverse direction at
the top of the prototype bridge, when subjected tothe simulated seismic excitation at the site of the JiLu Bridge (Test No.1: Ji-Lu Br. EW) and the simulated excitations of the anticipated Nankai earthquake at stations OSK008EW, OSK003EW, andOSK005EW (Test No.4: OSK008EW, No.9:
OSK003EW, and No.11: OSK005EW). Associatedwith all cases above, the seismic responses of thebridge model are in the linear range, where no
cracks occur in the tower in the experiments. Thus,
Fig. 19 show the cases where the experimental results are scaled up to those for the prototype bridge
based on the similarity ratios with respect to lengthand time shown in Table 7. In addition, to compare
the seismic responses of the case subjected to thelong-period excitations (OSK003EW, OSK005EW,
OSK008EW) with those subjected to the near-field
exitation (Kobe NS), Fig. 19 shows the same results
when subjected to the Kobe NS exitation from
nonlinear seismic analysis, in which the structuralmodeling of the bridge model is the same as that
adopted in Section 3. In the Kobe NS case, the seismic responses of the bridge model are also in theliner range.
From Fig. 19, it indicates that the maximum accelerations in the cases of the Ji-Lu Br. EW,
OSK003EW, OSK005EW, and OSK008EW are lessthan that in the case of the Kobe NS excitation. In
contrast, the maximum displacements in the cases of
the Ji-Lu Br. EW, OSK003EW, OSK005EW, andOSK008EW are larger than that in the case of theKobe NS excitation, especially in the case of
OSK008EW, where a maximum displacement of
1.35 m occurs at the top of the tower. This value ofmaximum displacement corresponds to a maximum
drift ratio of 1.35%, which is a large value corresponding with the response level of which seismic
behavior of the tower becomes nearly equal to be
nonlinear, describing the following figure.
Fig. 20 shows the relationship between the lateralforce and the lateral displacement at the top of theble test. Uni-lateral and bi-lateral shaking table tests
were conducted using the simulated ground excitation at the site of the Ji-Lu Bridge described in Section 2 and the excitations of the anticipated Nankai
earthquake at stations OSK003, OSK005, andOSK008 simulated by Kamae et al.5) The uni-lateralshaking was in the transverse direction of the bridge
model, which was subjected to the EW component
or the NS component of those excitations. The bilateral shaking was simultaneously in the transverseand longitudinal directions of the bridge model; thetransverse direction was subjected to the EW component of the above excitations and the longitudinal
direction was subjected to the NS component. The
seismic excitations were modified based on thesimilarity ratios with respect to length and timeshown in Table 7.
Fig. 17 shows the time histories of those excitations, and Fig. 18 shows their response spectra. Fig.
18 also shows the seismic response spectra of thebridge model when subjected to the NS componentof ground motions recorded at the JMA Kobe Observatory in the 1995 Hyogo-ken Nambu earthquake(Kobe NS) to clarify the difference of the response
spectra of long-period ground motions and typicalnear-field ground motion. From Fig. 18, the acceleration and velocity responses at the natural period993

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
0.1

Acceleration (G)Acceleration (G)

0.1
0.05
0

0.05
0

-0.05

-0.05

-0.1

-0.1

i) EW componentii) NS component(a) Simulated ground excitation at the site of the Ji-Lu Bridge
0.1
Acceleration (G)Acceleration (G)

0.1
0.05
0

0.05
0

-0.05

-0.05

-0.1

-0.1

0.1

0.1
Acceleration (G)Acceleration (G)i) EW componentii) NS component(b) Simulated ground excitation of the anticipated Nankai earthquake at station OSK008
0.05
0
-0.05

0.05
0

-0.05

-0.1

-0.1

i) EW componentii) NS component(c) Simulated ground excitation of the anticipated Nankai earthquake at station OSK003
0.1
Acceleration (G)Acceleration (G)

0.1
0.05
0
-0.05
-0.1
0

0.05
0

-0.05

5

10

15

20

25

-0.1

30

0

5

10

Time (sec)

15

20

25

30

Time (sec)

0.1
0.01
0.001

Dominant period of thebridge model ≈ 0.3 sec
1

Period (sec)

10

0.1

0.01

Dominant period of thebridge model ≈ 0.3 sec
0.1

1.0
0.1
0.01
0.001

0.1

Dominant period of thebridge model ≈ 0.3 sec
1

Period (sec)10ii) Velocity response spectra(a) EW component

10

Velocity response spectrum (m/s)

Acceleration response spectrum (G)i) Acceleration response spectra

1

Period (sec)100
Ji-Lu Bridge
OSK008OSK005
OSK003101
0.1

Dominant period of thebridge model ≈ 0.3 sec
1
Period (sec)10iii) Displacement response spectra

1.0

Displacement response spectrum (mm)

0.1

1.0

Displacement response spectrum (mm)1.0

Velocity response spectrum (m/s)

Acceleration response spectrum (G)i) EW componentii) NS component(d) Simulated ground excitation of the anticipated Nankai earthquake at station OSK005
Fig. 17 Input accelerations used for the shaking table tests.

100

0.1

0.01
Dominant period of thebridge model ≈ 0.3 sec
0.1

1
Period (sec)i) Acceleration response spectra

10Ji-Lu Bridge
OSK008OSK005
OSK003
Kobe NS

101
0.1

Dominant period of thebridge model ≈ 0.3 sec
1
Period (sec)10ii) Velocity response spectraiii) Displacement response spectra(b) NS component
Fig. 18 Response spectra for the bridge model when subjected to input ground motion.

994

Maximum displacement (m)Maximum acceleration (G)

0.8

0.6

0.4

0.2

0
Ji-Lu Br. OSK
008
Test No.1 No.4

OSK
003
No.9

1.5

1.5

1.0

1.0

0.5

0.5

0

OSK Kobe
005 NS
No.11

Ji-Lu Br. OSK OSK
008 003
Test No.1 No.4 No.9

OSK Kobe
NS
005
No.11

Maximum drift ratio (%)

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

0

100
80
60
40
20
0
-20
-40
-60
-80
-100

Lateral force at the tower top (N)Lateral force at the tower top (N)(a) Maximum acceleration response(b) Maximum displacement response
Fig. 19 Maximum acceleration and maximum displacement responses in the transverse direction at the top of the tower.

-20 -100
1020Lateral displacement at the tower
top (mm)

100
80
60
40
20
0
-20
-40
-60
-80
-100

-20 -100
1020Lateral displacement at the tower
top (mm)

Cracking at the height of 40.5mm
from the tower bottom(a) In the case of the excitation equal(b) In the case of two times the excitation of the OSK008 EW
to the OSK008 EW (Test No.4)
component (Test No.5)
Fig. 20 Lateral force versus lateral displacement relationship at the top of the tower, depending on the amplitudes of excitations.

tower for uni-lateral transverse shaking in the caseof the OSK008EW (Test No.4) and two times theexcitation of the OSK008 EW component (Test
No.5: 2 times-OSK008EW). The former case showsa linear response of the tower, previously shown in
Fig. 19, whereas the latter one shows a nonlinear
response that causes cracks in the tower model. As
mentioned above, although the relationship between
the lateral force and the lateral displacement in thecase of OSK008EW is limited in the linear range(Fig. 20(a)), its response level reaches almost same
one to be nonlinear hysteretic behavior that the caseof 2 times-OSK008EW shows (Fig. 20(b)).
The occurrence of larger displacement at the
tower top in the cases of the long-period ground motions than that in the case of the Kobe NS excitation,
results from the larger displacement response at the
tower top in the transverse direction on the 1st modeshown in Fig. 10 (a), due to the matching of thedominant natural period of the bridge model andthat of the long-period ground motions, shown in
Fig. 18. Thus, even though the acceleration responseof the long-period bridge does not become larger
within the range of 0.04 G to 0.06 G, the displacement response could become larger when subjectedto the long-period ground motions, and it is likelythat this mechanism causes the nonlinear hysteretic
behavior of the tower shown in Fig. 20(b).

(2) Residual displacement at the top of the tower
Fig. 21 shows the displacement responses at the
top of the tower for uni-lateral transverse shaking
equal to three times the excitation of the simulated
ground motion at the Ji-Lu Bridge (Test No.3: 3
times-Ji-Lu Br. EW), 2 times-OSK008EW (Test No.
5), and two times the excitation of the OSK008 NS
component (Test No.7: 2 times-OSK008NS). Fig.
21 also shows a comparison of the residual displacement at the top of the tower model with its
maximum displacement in the transverse direction.
In all cases, a crack occurred in the tower model; thevalues of the responses resulting from the tests are
not scaled up to in Fig. 21.
From Fig. 21, although the maximum displacements at the top of the tower for different groundmotions were nearly the same, namely, about 20
mm, the maximum residual displacements at the topof the tower were quite different depending on the
excitations applied. Whereas a slight residual displacement of 0.014% per unit of drift occurred in
the case of 3 times-Ji-Lu Br. EW (Test No.3), larger
residual displacements of 0.29% and 0.12% per unitof drift occurred for the case of 2 times-OSK008EW(Test No.5) and 2 times-OSK008NS (Test No.7),
respectively.
For the three cases described above, the relationship between the lateral force and the lateral dis-995

Uni-lateral transverse shaking of the threetimes larger excitation of the simulated
ground motion at the Ji-Lu Bridge (Test No.3)

30
15
0
-30
300

Uni-lateral transverse shaking of the twotimes larger excitation of the OSK008 EW
component (Test No.5)

15
0
-15
-30
0
30

Uni-lateral transverse shaking of the twotimes larger excitation of the OSK008 NS
component (Test No.7)

15

25

2.5

20

2.0

15

1.5

10

1.0

5

0.5

Maximum drift ratio (%)

Residual displacement
Max. displacement-15

Displacement (mm)Displacement (mm) Displacement (mm) Displacement (mm)

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

0
0

-15
-30
0

10

20
30
Time (sec)

40

50

0
2 timeslarger
OSK008 NS
Test No.7

3 times
2 timeslargerlargerJi-Lu Br. OSK008 EW
Test No.3 Test No.5(a) Displacement at the top of the tower (b) Comparison of residual displacement within the transverse direction
maximum displacement at the tower top
Fig. 21 Residual displacement, depending on the duration of the excitation.

0
-50

-100

stage1

50
0
-50

-100

-20 -100
10 20
Lateral displacement (mm)stage2100
Lateral force (N)50100Lateral force (N)100
Lateral force (N)Lateral force (N)

100

50
0
-50

-100

-20 -100
10 20
Lateral displacement (mm)

50
0
-50

-100

stage3-20 -100
10 20
Lateral displacement (mm)stage4-20 -100
10 20
Lateral displacement (mm)(a) Uni-lateral transverse shaking equal to three times the excitation of the simulated ground motion at the Ji-Lu Bridge (Test No.3)-50

stage1

50
0
-50

-100

-20 -100
10 20
Lateral displacement (mm)100
Lateral force (N)0Lateral force (N)

50

-100

100

100
Lateral force (N)Lateral force (N)

100

50
0

Residual disp. -50
occursstage2-100stage3

50
0
-50

-100

-20 -100
10 20
Lateral displacement (mm)-20 -100
10 20
Lateral displacement (mm)Residual disp.
slightly increases
stage4-20 -100
10 20
Lateral displacement (mm)(b) Uni-lateral transverse shaking equal to two times the excitation of the OSK008 EW component (Test No.5)-50

stage1-20 -100
10 20
Lateral displacement (mm)

50
0
-50

-100

100
Lateral force (N)0Lateral force (N)

50

-100

100

100
Lateral force (N)Lateral force (N)

100

50
0

Residual disp. -50
occursstage2-100stage3-20 -100
10 20
Lateral displacement (mm)-20 -100
10 20
Lateral displacement (mm)

50
0
-50

-100

Residual disp.
slightly increases
stage4-20 -100
10 20
Lateral displacement (mm)(c) Uni-lateral transverse shaking equal to two times the excitation of the OSK008 NS component (Test No.7)
Fig. 22 Lateral force versus lateral displacement relationship for four different stages in the response time series.

placement was computed for four different stages in
the response time series, as shown in Fig. 22: whenthe maximum displacement occurred when the mainlarge excitation subjected (stage 1), immediately

after stage 1 (stage 2), when the displacement response decreased after stage 2 (stage 3), and when
the displacement response increased after stage 3
due to the subsequent large excitation (stage 4).

996

1

Longitudinal displacement (mm)Longitudinal displacement (mm)

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Uni-lateral case

0.5
0
-0.5
-1

Cracking-20 -100
1020Transverse displacement (mm)1Bi-lateral case

0.5
0
-0.5
Cracking-1-20 -100
1020Transverse displacement (mm)(a) Uni-lateral transverse shaking equal to two times the (b) Bi-lateral transverse shaking of OSK008 EW
excitation of the OSK008 EW component (Test No.5)
and NS components (Test No.15)
Fig. 23 Comparison of longitudinal displacement versus transverse displacement relationship at the top of the tower, depending on
the uni-lateral excitations and the bi-lateral ones.

The residual displacement at the top of the tower
did not occur in stage 1 or stage 2 for the case of 3
times-Ji-Lu Br. EW (Test No.3), whereas those occurred in stage 2 for the cases of 2 timesOSK008EW (Test No.5) and 2 times-OSK008NS(Test No.7), and these residual displacements became continuous with those at the end of the displacement waveforms. Focusing on the increase of
the residual displacement after stage 2, in both cases
the large displacement response in stage 4 after 15
sec caused a slight increase in the residual displacement at the top of the tower.
The experimental results indicate that the subsequent large excitation after the maximum displacement had no effect on whether the residual displacement at the tower top occurred or not, whereas
it had a slight effect on the degree of increasing theresidual displacement at the tower top. Because theoccurrence of the residual displacement on structural components for the long-period bridge causes
the difficulty in the repair process after the bridge isdamaged, we must pay more attenetion to the increasing of the residual displacement at the tower
subjected to the subsequent large excitation which along-period ground motion contains.

For the cases described above, the relationships
between the longitudinal displacement and thetransverse displacement at the bottom and the top of
the tower at the maximum displacement, 4 waves
before the maximum displacement, and 1 wave after
the maximum displacement, were investigated; theresults, based on wave length units, are shown in
Figs. 24 and 25.
In the case of 2 times-OSK008EW (Test No.5),
the phase shift of the transverse response at the bottom and the top of the tower can be clearly observedin Fig. 24; the transverse displacement of the tower
top increased 3 to 4 waves after the displacement of
the tower bottom increased. In the case of BiOSK008 (Test No.15), the longitudinal displacement at the tower bottom varied by the range of± 0.5 mm that was larger than that in the case of 2
times-OSK008EW by the range of ± 0.2 mm, andthis caused the variation of the longitudinal displacement at the tower top and the coupled vibration
between the longitudinal and transverse directions at
the tower top. As a result of this, a large displacement vector was excited between the longitudinal
and transverse directions at the tower top shown in
Fig. 23(b); this caused the cracking of the tower.
Although the evidence is not compelling, it seems
likely that the 2nd mode of the bridge model, whichis the anti-symmetry one in the longitudinal direction shown in Table 6 and Fig. 10(b), contributes
the displacement response of the tower in the longitudinal direction and thus to couple the vibration
between the longitudinal and transverse directions at
the tower top. This is because the 2nd mode periodof the bridge model could be assumed to becomes
more than 1.0 sec when the 1st mode period reaches
to more than 3.0 sec. Therefore when the longperiod bridge is subjected to a long-period groundmotion, the coupling of the vibration between the
1st mode and others might occurs at the range of thenatural period of more than 1.0 sec.

(3) Uni-lateral shaking versus bi-lateral shaking
Fig. 23 shows the relationship between the longitudinal displacement and the transverse displacement at the top of the tower for the case of 2 timesOSK008EW (Test No.5) and for bi-lateral transverse and longitudinal shaking equal to the OSK008
EW and NS components (Test No.15: Bi-OSK008).
In the case of 2 times-OSK008EW (Test No.5), a
maximum displacement of 21.2 mm occurred at the
top of the tower in the transverse direction, whichcaused a crack in the tower model. In contrast, in thecase of Bi-OSK008 (Test No.15), when the transverse displacement of 15.0 mm was accompanied by
the longitudinal one of 0.6 mm, the crack occurredin the tower model.

997

Longitudinal
displacement (mm)

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12

1

1

0.5
0

-1

1

1

0.5

0.5

0.5

0.5

0.5

0

0

0

0

0

4 waves -0.5
before-1-20 -10
0 10 20-0.5-20 -10

Initial point
Terminal point

1

3 waves -0.5
before-1
0 10 20-20 -10

1

-0.5
-0.5
Maximum
2 waves -0.5
1 wavedisplacement
beforebefore-1-1-1-20 -10 0 10 20-20 -10 0 10 20-20 -10
0 10 20
Transverse displacement (mm)1 waveafter
0 10 20(a) At the top of the tower
Longitudinal
displacement (mm)1

4 waves
before0.5

1

3 waves
before0.5

1

1

2 waves
before0.5

0.5

1 wavebefore

0

0

0

0

-0.5

-0.5

-0.5

-0.5

-1
10 -10-1
10 -10-1
0 5 10 -10 -5
0Transverse displacement (mm)

-1
-10

-5

0

5

-5

0

5

-5

5

Initial point
Terminal point

1
0.5

10

1

Maximum
displacement

0

0

-0.5

-0.5

-1
-10

-5

0

5

1 wave
after

0.5

10

-1
-10

-5

0

5

10

(b) At the bottom of the tower
Fig. 24 Relationship between longitudinal displacement and transverse displacement for uni-lateral transverse shaking equal to twotimes the excitation of the OSK008 EW component (Test No.5).

Longitudinal
displacement (mm)1

4 waves
before0.5

1

3 wavebefore0.5

1

1

2 waves
before0.5

0.5

1 wavebeforeInitial point
Terminal point

1

Maximum
displacement

0.5

1

0

0

0

0

0

0

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-1

-20 -10

0

10 20

-1

-20 -10

0

10 20

-1

-20 -10-1
0 10 20-20 -10 0 10 20
Transverse displacement (mm)-1

-20 -100

10 20

1 wave
after

0.5

-1

-20 -100

10 20Longitudinal
displacement (mm)(a) At the top of the tower
1

1

1

1

1

0.5

0.5

0.5

0.5

0.5

0

0

0

0

0

-0.5

-0.5

-1
-10

-5

4 waves
before-1
0
5 10 -10-5

3 wave -0.5
before-1
0 5 10 -10

1 wave -0.5
before-1-1
0 5 10 -10 -50
5 10 -10
Transverse displacement (mm)2 waves
before-5Initial point
Terminal point

1
0.5
0

-0.5

Maximum
displacement
-5

0

5

-0.5

-1
10 -10-5

1 waveafter
0 5 10(b) At the bottom of the tower
Fig. 25 Relationship between longitudinal displacement and transverse displacement for bi-lateral transverse shaking in the case of
the OSK008 EW and NS components (Test No.15).

(4) Coupled seismic response between the tower
and the cables
Fig. 26 shows the tension variation of the cables,
and the relationship between the prestressed tension
strength and the maximum tension strength for thecase of Bi-OSK008 (Test No.15).
The large maximum displacement of the tower
top in the transverse direction, that is 15.0 mm (Figs.
23(b), 26(b)), caused a drift in the variation of eachcable tension (Fig. 26(a)), and the damage to thetower model caused a maximum tension variation of
19.8% in cable 1, which was positioned closest to
the tower, and a maximum tension variation of
9.24% in cable 4, which was positioned farthestfrom the tower (Fig. 26(c)).
This indicates that the large displacement vector
at the tower top with the coupling of the vibration

998

modes in the longitudinal and transverse directions
described previously, induced the tension variationof the cables. This resulted from the large transverse
component of the displacement vector at the tower
top due to the matching of the dominant natural period of the bridge model and that of the long-period
ground motions, shown in Fig. 18 as well as in thecase of the uni-lateral shaking. It is possible thatlarger tension variation of the cables is induced
when the transverse displacement at the tower top
becomes larger, thus the coupling response between
the tower and the cables should be carefully given
attention to when subjected to the long-period
ground motion.

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Max. disp.= 15.0mm
Dr = 1.50%

Cable tension
variation (N)Cable tension
variation (N)105Cable 1

Variation ofcable tension

0
-5
-100
10

4

5

50

5

Cable 30Tension (N)Cable tension
variation (N)

1

60

-10
10 0

-5
0

10
Cable tension
variation (N)2(b) Maximum displacement of tower top
in the transverse direction

0
-5

-10

3

Cable 2

5

40
30
20

Cable 40

10Max. tension
Prestressed tension

-5
-10

0

10

20
30
Time (sec)4050(a) Variation of cable tension strength

0

1

2

3
4
Cable No.
(c) Comparison of maximum cable tension withprestressed cable tension

Fig. 26 Seismic response of the cables for bi-lateral shaking in the case of the OSK008 excitation (Test No.15).

amplified.
2) From the tests, larger maximum displacements
were found at the tower top for the long-period
excitations compared with that obtained from theseismic response analysis using the JMA Kobe record (near-field excitation). This resulted fromlarger displacement response at the tower top in
the transverse direction, which maximum drift ratio becomes more than 1 %, depending on the 1stmode of the bridge model, due to the matching of
the dominant natural period of the bridge modeland that of the long-period ground motions. Thus,
even though the acceleration response of the longperiod bridge is not amplified in the range ofabout 0.05 G, the displacement response could become larger when subjected to the long-period
ground motions. Although this mechanism isqualitatively quite reasonable based on linear vibration theory, it is more important to note that
this mechanism may cause the nonlinear hysteretic
behavior of the tower bottom and the exceeding
tension variation of the cables.
3) The subsequent large excitation after the maximum displacement at the tower top did not affectthe occurrence of the residual displacement of thetower, whereas it slightly affected the degree ofincreasing the residual displacement. The occurrence of the residual displacement on structuralcomponents for the long-period bridge causes thedifficulty in the repair process after the bridge isdamaged, then we must pay more attenetion to theincreasing of the residual displacement at the
tower subjected to the subsequent large excitation

6. CONCLUSIONSIn this study the mechanisms associated with theseismic response of a PC cable-stayed bridge whensubjected to a long-period ground motion wereclarified based on seismic response analyses andshaking table tests considering the similarity law.
This study defined the ‘long-period’ of ground motions as the period of more than 2.0 sec or 2.5 sec.
The natural period of the subject structures wasfrom 2.0 sec to 3.0 sec. The simulated long-period
ground motions in the 1999 Chi-Chi, Taiwan earthquake and the anticipated Nankai earthquake wereused as the input ground motions in the numericalanalyses and the shaking table tests. The following
conclusions were obtained from the study:1) The seismic excitation at the site of the Ji-Lu
Bridge, which was damaged in the 1999 Chi-Chi,
Taiwan earthquake, was simulated by the finite
differential method. Using the simulated longperiod ground motions, the damage to the bridge
was assessed from the nonlinear seismic analysis.
From this analysis, damage beyond the crack leveloccurred at the bottom of the tower. However,yielding-level damage did not occur at the bottomof the tower, although yielding of the longitudinal
reinforcements and spalling-off of the cover concrete actually occurred. The reason for this discrepancy is that the simulated excitation at the siteof the Ji-Lu Bridge contained long-period components of more than 2.0 sec, and its seismic response around the period of 2.005 sec, which isthe dominant natural period of the bridge, was not999

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12of the long-period ground motion.
4) It seems likely that the 2nd mode of the bridge
model, which was the anti-symmetry one in thelongitudinal direction, contributed the displacement response of the tower in the longitudinal direction and thus to couple the vibration between
the longitudinal and transverse directions at the
tower top. This excited a large displacement vector in the longitudinal and transverse directions at
the tower top; this caused the cracking of thetower. Therefore when the long-period bridge issubjected to a long-period ground motion, thecoupling of the vibration between the 1st modeand others might occurs at the range of the natural
period of more than 1.0 sec, which is relatively
higher natural period than that of the other structural-typed bridges.
5) Above large displacement vector at the tower top
with the coupling of the vibration modes in thelongitudinal and transverse directions induced thetension variation of the cables. Since it is possiblethat larger tension variation of the cables is induced when the transverse displacement at the
tower top becomes larger, the coupling response
between the tower and the cables should be given
much attention to when subjected to the longperiod ground motion.
ACKNOWLEDGMENT: This research was sponsored by the National Research Institute for Earth
Science and Disaster Prevention (NIED) under agrant provided for seismic experimental research on
bridges titled ‘International Joint Model Research
for the Application of the Full-Size ThreeDimensional Vibration Destruction Facility (EDefense)’. The authors deeply appreciate research
information and valuable assistance provided by Dr.
H. Sekiguchi at the Active Fault Research Center,
National Institute of Advanced Industrial Scienceand Technology, regarding the numerical simulations of the ground motion at the Ji-Lu Bridge, andthe valuable assistance and support of Dr. S. Aoi
and Dr. H. Fujiwara at NIED, regarding the finite
differential modeling for the simulation of the longperiod seismic excitations. The authors are also
deeply grateful for research information and valuable assistance provided by Professor K. Kosa andMr. H. Abe at the Kyushu Institute of Technology,
Dr. K. Tasaki at Nippon Engineering Consultants
Co., Ltd., Mr. H. Ukon at the Hyogo Earthquake
Engineering Research Center, NIED, and Dr. M.
Yabe at Chodai, Ltd., regarding the modeling of thePC cable-stayed bridge. The authors also speciallythank Professor K. Kamae and Dr. H. Kawabe at
Research Reactor Institute, Kyoto University, forproviding the simulated waveforms of the antici-

pated Nankai earthquake. Finally, we are grateful to
Dr. A. Numata, Mr. T. Ikeda, Mr. K. Taguchi andthe members of Disaster Prevention R&D ResearchInstitute, Tobishima Corporation, for the use of experimental facilities, and for valuable assistance andsupport.
REFERENCES
1) For instance, Irikura, K.: Long-Period Ground Motions from
Devastating Great Earthquakes and Action Plans for Earthquake Disaster Mitigation, Chikyu Monthly, No.55, pp. 6-16,
2006 (in Japanese).
2) Kawashima, K., Iemura, H., Shoji, G. and Iwata, S.: Damageof Transportation Facilities in the Chi Chi, Taiwan Earthquake, Technical Report on TIT Earthquake Engineering Research Group, TIT/EERG 99-8, 1999 (in Japanese).
3) Kosa, K., Takahashi, Y., Yamaguchi, E., and Nomura, T.:
Analysis of Bridges Damaged by Seismic Motion in the ChiChi Earthquake, Bridges and Foundations, No. 9, pp. 79-86,
2002 (in Japanese).
4) Tasaki, K., Kosa, K., Ikeda, T. and Ogo, M.: Detailed Investigation of PC Cable-Stayed Bridge (Ji-Ji-Da Bridge) Damaged to the Taiwan Chi-Chi Earthquake, Journal of Structural Engineering, JSCE, Vol.50A, pp. 487-494, 2004 (inJapanese).
5) Kamae, K., Kawabe, H. and Irikura, K.: Strong Ground Motion Prediction for Huge Subduction Earthquakes Using a
Characterized Source Model and Several Simulation Techniques, 13th World Conference on Earthquake Engineering,
Vancouver, B.C., Canada, Paper No. 655 (CD-ROM), 2004.
6) Otsuka, H., Somerville, P.G. and Sato, T.: Estimation of
Broadband Strong Ground Motions Considering Uncertainty
of Fault Parameters, JSCE Journal of Structural and Earthquake Engineering, No. 584, I-42, pp. 185-200, 1998 (inJapanese).
7) Komori, K., Kikkawa, H., Odagiri, N., Kinoshita, T.,
Mizoguchi, T., Fujino, Y. and Yabe, M.: Basic Principles andDesign Ground Motions in Seismic Retrofit Design of Large
Cable-Supported Bridges on the Tokyo Metropolitan Expressway, JSCE Journal of Structural and Earthquake Engineering, No. 794, I-72, pp. 1-19, 2005.7 (in Japanese).
8) Nazmy, A. S. and Abdel-Ghaffar, A. M.: Non-Linear Earthquake-Response Analysis of Long-Span Cable-Stayed
Bridges: Theory, Earthquake Engineering and Structural
Dynamics, Vol. 19, pp. 45-62, 1990.
9) Nazmy, A. S. and Abdel-Ghaffar, A. M.: Non-Linear Earthquake-Response Analysis of Long-Span Cable-Stayed
Bridges: Applications, Earthquake Engineering and Structural Dynamics, Vol. 19, pp. 63-76, 1990.
10) Vilaverde, R. and Martin, S. C.: Passive Seismic Control ofCable-Stayed Bridges with Damped Resonant Appendages,
Earthquake Engineering and Structural Dynamics, Vol. 24,
pp. 233-246, 1995.
11) Kawashima, K., Unjoh, S., and Tunomoto, M.: Estimationof Damping Ratio of Cable-Stayed Bridges for Seismic Design, Journal of Structural Engineering, ASCE, Vol. 119, No.
4, pp. 1015-1031, 1993.
12) Kitazawa, M., Ishizaki, H., Emi, S. and Nishimori, K.:
Characteristics of Earthquake Responses and Aseismic Design on the Long-Period Cable-Stayed Bridge (Higashi-Kobe
Bridge) with All Free Movable Shoes in Longitudinal Direction, JSCE Journal of Structural and Earthquake Engineering, No. 422, I-14, pp. 343-352, 1990 (in Japanese).
13) Tai, J.C., and Liou, Y.Y.: Retrofit on Ji-Lu Cable Stayed

1000

Doboku Gakkai Ronbunshuu A Vol.64 No.4, 982-1001, 2008. 12
Bridge after 921 Chi-Chi Earthquake, Proceedings of theSecond International Workshop on Mitigation of Seismic Effects on Transportation Structures, National Center for Research on Earthquake Engineering, Taipei, Taiwan, R.O.C.,
pp. 65-79, 2000.
14) Sekiguchi, H. and Iwata, T.: The Source Process of the1999 Chi-Chi, Taiwan, Earthquake in Semi-Long Period (220s), Active Fault and Old Earthquake Research Report, No.
1, pp. 315-324, 2001 (in Japanese).
15) Chung, J-K. and Yeh, Y.T.:Shallow Crustal Structure from
Short-Period Rayleigh-Wave Dispersion Data in Southwestern Taiwan, Bulletin of the Seismological Society of America,
Vol. 87, No. 2, pp. 370-382, 1997.
16) Ido, Y. and Shoji, G.: Evaluation of Ground Motions at the
Site of the Ji-Lu Bridge in the 1999 Chi-Chi, Taiwan Earthquake, Proceedings of the 8th Symposium on Ductility Design
Method for Bridges, JSCE, pp. 441-446, 2005 (in Japanese).
17) Tokimatsu, T. and Sekiguchi, T.: S wave Velocity Structureof the Observatory Stations in the 1999 Chi-Chi, Taiwan
Earthquake estimated from Microwave Observation and its
Effect of the Structural Seismic Damage, Journal of Structural and Construction Engineering, Transaction AIJ, No.
550, pp. 65-70, 2001 (in Japanese).
18) Aoi, S. and Fujiwara, H.: 3-D Fourth-Order FiniteDifference Seismograms Using Discontinuous Grids, Proceedings of the Tenth Japan Earthquake Engineering Symposium, Vol. 1, pp. 875-880, 1998 (in Japanese).
19) Aoi, S. and Fujiwara, H.: 3-D Finite Difference Method
Using Discontinuous Grids, Bulletin of the Seismological Society of America, Vol. 89, pp. 918-930, 1999.
20) Graves, R.W.: Simulating Seismic Wave Propagation in 3D
Elastic Media Using Staggered-Grid Finite Differences, Bulletin of the Seismological Society of America, Vol. 86, No. 4,
pp. 1091-1106, 1996.
21) Levander, A.R.: Fourth-Order Finite-Difference P-SV Seismograms, Geophysics, Vol. 53, No. 11, pp. 1425-1436, 1988.
22) Buell, J.C.: A Hybrid Numerical Method for ThreeDimensional Spatially-Developing Free-Shear Flows, Journal of Computational Physics, Vol.95, pp. 313-338, 1991.
23) Takenaka, H.: Computational Methods for Seismic Wave
Propagation in Complex Subsurface Structures, Journal of the
Seismological Society of Japan, Vol. 46, pp. 191-205, 1993

(in Japanese).
24) Cerjan, C., Kosloff, D., Kosloff, R., and Reshef, M.: A
Nonreflecting Boundary Condition for Discrete Acoustic andElastic Wave Equations, Geophysics, Vol. 50, No. 4, pp. 705708, 1985.
25) Clayton, R. and Engquist, B.: Absorbing Boundary Conditions for Acoustic and Elastic Wave Equations, Bulletin of the
Seismological Society of America, Vol. 67, No. 6, pp. 15291540, 1977.
26) Lee, W.H.K., Shin, T.C., Kuo, K.W., and Chen, K.C.: CWB
Free-Field Strong-Motion Data from the 921 Chi-Chi Earthquake: Volume 1. Digital Acceleration Files on CD-ROM,
Pre-Publication Version, Seismology Center, Central
Weather Bureau, Taipei, Taiwan, 1999.
27) Ranbiner, L.R., McClellan, J.H. and Parks, T.W.: FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation, Proceedings of the IEEE, Vol. 63, No. 4, pp.
595-610, 1975.
28) Takeda, T., Sozen, M. A. and Nielsen, N. N. : Reinforced
Concrete Response to Simulated Earthquakes, Proceedings of
3rd Japan Earthquake Symposium, pp.357-364, 1970.
29) Abe, H.: Damage Assessment of Ji-Ji-Da Bridge (PC Cable-Stayed Bridge) suffered from the 1999 Chi-Chi, Taiwan
Earthquake, Undergraduate Thesis, Kyushu Institute of Technology, 2004 (in Japanese).
30) Sakai, Y., Tanaka, T., Shiino, A., Tokui, N., Yamauchi, N.,
Sanada, Y., Nakano, Y., Suwa, H. and Fukuyama, H.: Simplified Vibration Experiment of RC Structure subjected to Various Input Ground Motions, Proceedings of the JAEE Annual
Meeting-2004, pp. 424-425, 2004 (in Japanese).
31) Shimizu, K., Ujiie, T., Kanakubo, T. and Hikita, T.: Evaluation of Shear Capacity of PVA-ECC Beam, JCI Annual Convention Proceedings, Vol. 27, No. 2, pp. 1333-1338, 2005 (inJapanese).
32) Billington, S.L. and Kesner, K.E.: Cyclic Response of Ductile Fiber-Reinforced Cement-Based Composites, Proceedings of the Fourth International Workshop on High Performance Fiber Reinforced Cement Composites, HPFRCC4, Ann
Arbor, USA, pp. 363-378, 2003.

1001(Received April 24, 2007)