Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanDAMAGE ANALYSIS OF SHINKANSEN VIADUCTS
DURING THE 2011 GREAT EAST JAPAN
EARTHQUAKE
Mitsuyoshi AKIYAMA1 and Keita MIZUNO2
1

Professor, Department of Civil and Environmental Engineering, Waseda University,
Tokyo, Japan, akiyama617@waseda.jp
2
Department of Civil and Environmental Engineering, Waseda University,
Tokyo, Japan, 7151@ruri.waseda.jp

ABSTRACT: Retrofitted bridge fragility curves provide a powerful tool for assessing
the effect of retrofit measures on seismic performance under a range of loading levels.
Nonlinear dynamic analyses to develop the fragility curves of the steel-jacketed RC
columns of the Shinkansen viaducts are performed in a Monte Carlo Simulation. The
fragility curves in this study are represented by a lognormal distribution as a function ofpeak ground acceleration (PGA) or response acceleration. The improvement of seismic
performance from retrofitting is quantified by comparing the fragility curve of the
as-built viaduct with that of the retrofitted viaduct.
Key Words: 2011 Great East Japan earthquake, fragility curve, Monte Carlo Simulation,
Shinkansen viaduct, steel jacketing, seismic reliability

INTRODUCTION
Bridges may be susceptible to damage during an earthquake event, particularly if they were designed
without adequate seismic detailing. Reinforced concrete (RC) columns built using earlier designs often
lack flexural strength, flexural ductility and/or shear strength. When these components are subjected tostrong ground motions, they have the potential to exhibit brittle failure. Several recent destructive
earthquakes in Japan (1995 Hyogoken-Nanbu earthquake, 2003 Sanriku-Minami earthquake, and 2004
Niigata-ken-Chuetsu earthquake) inflicted various levels of damage on the Shinkansen viaducts. The
investigation of these negative consequences gave rise to serious discussions about seismic design
philosophy and to extensive research activity on the retrofit of existing bridges. The seismic design
methodology for new bridges was also improved. General column retrofits often include some type ofencasement to improve the shear or flexural strength, flexural confinement and ductility capacity. Steeljackets are a common measure.
The Tohoku Shinkansen viaducts in eastern Japan, which were designed using specifications
published in the 1970s, were damaged due to the 2003 Sanriku-Minami Earthquake because of theinadequacies of the shear design of RC components. After that earthquake, the RC bridge piers of the
Tohoku Shinkansen viaducts were retrofitted with steel jacketing to prevent brittle failure from asevere earthquake and to enhance the ductility capacity. This work was finished before the 2011 Great
East Japan earthquake. As reported in a JSCE damage investigation (Kawashima et al., 2011), theretrofitted Shinkansen viaducts experienced no damage, and the effectiveness of the seismic retrofit
involving the application of steel jacketing to RC columns was demonstrated. However, there is a lackof understanding of the impact of these retrofits on the vulnerability of the viaduct. It is important torecognize the relationship between the damage to the Shinkansen viaduct with retrofitted RC columns

1353

Super express (Shinkansen)
GirderSide columns

GirderCenter columns
Side columns

Single story RC moment resisting frame

Figure 1. Single-story RC moment-resisting frame pier with a Gerber girder on both sides
and the ground motion intensity.
Seismic fragility curves are essential tools for assessing the vulnerability of viaducts. These curves
describe the probability that the actual damage to a viaduct exceeds the damage criteria when the
structure is subjected to a specific ground motion intensity. Fragility curves can offer a means ofcommunicating the probability of damage over a range of potential earthquake ground motion
intensities. This information is essential for seismic risk management and decision making on retrofit
and mitigation strategies. Empirical fragility curves based on bridge damage data from pastearthquakes have been developed for as-built bridges (e.g., Shinozuka et al., 2000). However, as aresult of the limited empirical data available, developing the fragility curves for retrofitted bridges
based on damage investigation is impossible. In the absence of adequate empirical data, analyticalmethods have been used to develop the curves (e.g., Karim and Yamazaki, 2003). Analytically derived
fragility curves for retrofitted road bridges were developed by Kim and Shinozuka (2004) and Padgett
and DesRoches (2007a, 2008, 2009). Demand and capacity are compared in a fragility analysis. In
previous studies on analytically computed fragility curves, the demands were evaluated by a nonlinear
dynamic analysis of the retrofitted bridge, and the capacities of each component were defined based on
the results from past experiments and the results of an expert opinion survey (Padgett and DesRoches
2007b). In their fragility analysis, Padgett and DesRoches (2008) used the curvature ductility
capacities of steel-jacketed columns with median values of 9.35 for slight damage, 17.7 for moderate
damage, 26.1 for extensive damage and 30.2 for complete damage. However, these values could not beapplied to develop the fragility curves of the Shinkansen viaducts in Japan with steel-jacketed RC
columns.
In this paper, the moment-curvature relations of RC columns with steel jacketing based on
experimental results are used. The limit states for the fragility analysis of the as-built and retrofitted
viaducts are defined. The improvement due to steel jacketing is quantified by comparing the fragility
curves of the viaduct before and after retrofit.

DAMAGE INVESTIGATION OF THE SHINKANSEN VIADUCTS WITH RETROFITTED
RC BRIDGE PIERS SUBJECTED TO THE 2011 GREAT EAST JAPAN EARTHQUAKE
Seismic Retrofit Program of the Shinkansen Viaducts
Tohoku Shinkansen entered service in 1982 between Omiya and Morioka Stations. Because

1354

300

200
100

Time (sec)

0
-100
-200

0

50

100

150

200

250

300

2003 Sanriku-Minami earthquake

Acceleration (gal)Acceleration (gal)

300

200
100

Time (sec)

0
-100

0

50

-200

100

150

200

250

300

2011 Gear East Japan earthquake

-300

-300

Figure 2. Comparison of the acceleration time history measured near the No. 5 Inohana viaducts
during the 2003 Sanriku-Minami earthquake and the 2011 Great East Japan earthquake

Response acceleration (gal)1000

h = 5%
800

2003 Sanriku-Minami earthquake2011 Gear East Japan earthquake

600
400
200
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Natural period (sec)Figure 3. Response accelerations during the 2003 Sanriku Minami earthquake andthe 2011 Great East Japan earthquake measured near the No. 5 Inohana viaduct
the Shinkansen viaducts were designed prior to the occurrence of the 1978 Miyagi-ken-oki earthquake,they have less shear reinforcement than is required by current code. Some viaducts of the Tohoku
Shinkansen between the Morioka and Mizusawa-Esashi stations in Iwate-ken were extensively
damaged during the 2003 Sanriku-Minami earthquake (JSCE, 2004).
It should be noted that all the viaducts that suffered damage during the 2011 Great East Japan
earthquake had not yet been retrofitted. Most viaducts in Iwate-ken were single-story RC
moment-resisting frames with a Gerber girder on both sides, as shown in Figure 1. Damage wasconcentrated at the side columns of the viaduct during the 2003 Sanriku-Minami earthquake. Because
the side columns were made shorter than the center columns to fit under the Gerber girder, the ratio of
the shear strength to the flexural strength was smaller in the side columns than in the center columns,
which led to shear failure in the side columns.
After the 2004 Niigata-ken Chuetsu earthquake, the first seismic retrofit program was initiated for
the Shinkansen viaducts, including the Tohoku Shinkansen. The objectives of the program were toenhance the seismic performance of the RC columns, which had insufficient shear strength. The
program was completed in 2007 after retrofitting 12,500 columns. In 2009, the second retrofit programfor enhancing the flexural strength and ductile capacity of the RC columns was initiated.
The No. 5 Inohana Viaducts
Figures 2 and 3 compare the acceleration time history and 5% damping response accelerations of the2003 Sanriku-Minami earthquake with those of the 2011 Great East Japan earthquake. Both groundmotions were measured at the same site near the No. 5 Inohana viaducts. As shown in Figure 2, theduration of the ground motion was very different between the 2003 Sanriku-Minami earthquake andthe 2011 Great East Japan earthquake. However, the peak ground accelerations (PGAs) were almost

1355

Taken af ter 2011 Great East Japan Earthquake

Taken af ter 2003 Sanriku-Minami Earthquake

GirderTo Morioka Sta.

GirderSide column of R14

Side column of R14

Side column of R13

Side column of R13

Taken af ter 2011 Great East Japan Earthquake

Side column of R15

Taken af ter 2003 Sanriku-Minami Earthquake

Figure 4. R13 to R15 of the No. 5 Inohana viaduct taken after the 2003 Sanriku-Minami earthquake
and the 2011 Great East Japan earthquake(Note: the viaducts were retrofitted before the 2011 Great East Japan earthquake)the same. In addition, as shown in Figure 3, because the fundamental natural period of a single-story
RC rigid frame ranges between 0.4 s and 0.6 s, it is reasonable to assume that the response
accelerations of the No. 5 Inohana viaducts were nearly the same between the 2003 Sanriku-Minami
earthquake and the 2011 Great East Japan earthquake.
Figure 4 shows the damaged states of the No. 5 Inohana viaducts taken after the 2003
Sanriku-Minami earthquake and the 2011 Great East Japan earthquake, respectively. Because of
deficiencies in the number of ties used to prevent brittle failure, the RC columns of the No. 5 Inohana
viaduct failed via shearing during the 2003 Sanriku-Minami earthquake. Under the first retrofit
program described above, the viaducts were retrofitted by means of steel jackets for the RC columns
so that they had sufficient shear capacity. Steel jackets with a thickness of 6 mm were used, and thegap between the as-built RC column and the steel jacket was approximately 30 mm. The gap was
filled with a low-strength and highly liquid material. For road bridges in Japan, a steel jacket is used toincrease the shear and flexural strengths and the ductile capacity (Kawashima, 2000). To increase theflexural strength, anchor bolts were provided to connect the bottom of the steel jacket to the footing.
However, under the first program for the Shinkansen viaducts, because the steel jacket was only used
to increase the shear strength and ductile capacity, it was not anchored to other components.
The retrofitted columns of the viaducts performed well, with almost no damage during the 2011
Great East Japan earthquake. The effectiveness of seismic retrofitting using steel jacketing to prevent
significant damage to the Shinkansen viaducts was demonstrated.

FRAGILITY ANALYSIS OF THE SHINKANSEN VIADUCTS
Basic Equations for Developing Fragility Curves for As-Built and Retrofitted Viaducts
Fragility is defined as the conditional probability of the limit state gi ≤ 0 (representing the seismic

1356

560

longitudinal rebar with diameter of 29 mm
tie with diameter of 13 mm

1050
425
425

1050
425
425

1850

1850

1850

1850

78
694 850
78
78

425
425

425
425

694

78
unit (mm)850

Cross-section of the RC columns in the plastic hinge

Figure 5. Analytical modeling for a single-story RC moment-resisting frame pierMoment M

idealized skeleton curve

χ4Mu
My

⎛θ
⎞
k r = k y ⎜ max ⎟⎜ χ 2θ ′y ⎟
⎝
⎠

−0.5

ky

Rotation θ

θy

χ2θ’y

θmax

χ3θu

Figure 6. Moment and rotation relationship of a plastic hinge for an RC column with a steel jacket
demand placed on the structure exceeding its capacity for a given level of seismic intensity Γ, such as
PGA and response acceleration). This can be expressed as follows:
Fragility = P[g i ≤ 0 | Γ = γ ](1)

In this study, the limit states used in Equation (1) are determined for the as-built viaduct, as shown in
the following equations:
g1 = χ1 (Vc + Vs ) − VD ,bg 2 = χ 2θ y′ ,b − θ D ,b
g 3 = χ 3θ u ,b − θ D ,b

(2)
(3)
(4)

where Vc and Vs are the shear strengths contributed by the concrete and the shear reinforcement,
respectively; VD,b and θD,b are the peak shear forces of the RC column of the as-built viaduct and therotation demand of the plastic hinge of the RC column of the as-built viaduct, respectively; θ’y,b andθu,b are the yielding and ultimate rotations of the plastic hinge of the RC column of the as-built viaduct,
respectively; and χ1, χ2, and χ3 are the lognormal random variables representing the model uncertainties
associated with the estimation of Vc+Vs, θy,b, and θu,b, respectively. The shear strength Vc+Vs in
Equation (1) and the statistics of χ1 are provided by Akiyama et al. (2010).
The Shinkansen viaducts were retrofitted by means of steel jacketing of the as-built RC columns.
Because the viaduct has sufficient shear resistance after retrofitting, the limit state associated with1357

shear failure was not considered for the retrofitted viaduct. The limit states for the retrofitted viaduct
are provided by
g 4 = χ 2θ y′ , a − θ D ,ag 5 = χ 3θ u ,a − θ D , a

(5)
(6)

where θ’y,a and θu,a are the yielding and ultimate rotation capacity of the plastic hinge of thesteel-jacketed RC column, respectively, and θD,a is the rotation demand on the plastic hinge of thesteel-jacketed RC column.
The fragility in Equation (1) is estimated by a Monte Carlo Simulation (MCS) and determinedfrom the ratio of the number of times gi (i=1, 2, 3, 4, 5) ≤ 0 (i.e., demand exceeds capacity) to the total
number of MCSs. The variables VD,b, θD,b and, θD,a in Equations (2) to (6) are calculated by a nonlinear
dynamic analysis using a number of ground motions, as described later. If the fragility P[gi ≤ 0 |Γ=γ]
and seismic intensity γ relationship is modeled as a lognormal distribution based on the results of thefragility analysis using MCSs, then the fragility curve is represented by⎡ ln⎛ γ ⎞ ⎤⎢ ⎜ λ ⎟⎠ ⎥F (γ ) = Φ ⎢ ⎝
⎥
⎢ ς
⎥
⎣
⎦

(7)

where λ and ζ are the median and log-standard deviation of the fragility curve and Φ[·] is thestandard-normal distribution function. The parameters used to determine the lognormal distribution,(median λ and log-standard deviation ζ), are estimated by the method of maximum likelihood(Shinozuka et al., 2000).
The difference is negligible between P[gi ≤ 0 |Γ=γ] (provided by MSC) and F (γ) (in Equation (7))
at each seismic intensity γ. The number of samples was set to 1,000.
Dynamic Response Analysis of the Shinkansen Viaducts
The side columns of the single-story RC moment-resisting frame R15 of the No. 5 Inohana viaducts,
as shown in Figure 4, are analyzed in this study (hereafter referred to as the “frame pier”). The seismic
behavior of the frame pier is captured in the transverse direction. Figure 5 shows a two-dimensional
response model to develop the fragility curves before and after the column retrofitting with a steel
jacket. Within the hypothesis of a stiff soil, the bases of the frame piers are assumed to be fully fixed.
The column is modeled as an elastic zone with a pair of plastic hinges at each end of the column. Each
plastic hinge is modeled to consist of a nonlinear rotational spring, as shown in Figure 5. Figure 6
shows that the relationship between the moment and the rotation of the plastic hinge has a monotonic
envelope, represented by the two lines, and that the stiffness beyond the yielding point is assumed to
be zero. The rotation at the yielding point is provided byθ y′ = (M u M y )θ y(8)where Mu is the ultimate moment of the plastic hinge of the as-built or retrofitted column and My andθy are the moment and rotation of the as-built or retrofitted column when the strain in the extreme
tensile rebar reaches its yield point, respectively.
The rotation capacity θu,a is provided by Tamai et al. (1996) as follows:θ u ,a =4.66t+ 0.024bwhere t is the thickness of the steel jacket and b is the cross-sectional width of the as-built column.

1358

(9)

0.012350

Test / Computed
Mean: 0.936
COV: 29.8%

Test results of Mu (tf m)

Test results of θy,a (rad)

0.015

0.009
0.006
0.003
0.000
0.000

Test / Computed
Mean: 1.21
COV: 19.2%

300
250
200
150
100
50
0

0.003

0.006

0.009

0.012

0.015

0

50

Computed results of θy,a (rad)Test results of θu,,a (rad)

0.16

100

150

200

250

300

350

Computed results of Mu (tf m)

Test / Computed
Mean: 1.09
COV: 17.8%

0.12

0.08

0.04

0.00
0.00

0.04

0.08

0.12

0.16

Computed results of θu,a (rad)Figure 7. Comparison of the computed and experimental resultsfrom the evaluation of θ’y,a, θu,a, and Mu

6000

12000

5000

h = 5%
Response Acceleration (gal)Response acceleration (gal)h = 5%
10000

PGA = 1000 gal

4000
3000
2000
1000
0

Sa (T1, h) = 1000 gal

8000
6000
4000
2000
0

0.0

0.5

1.0

1.5

2.0

Natural period (sec)

0.0

0.5

1.0

1.5

Natural period (sec)Figure 8. Response acceleration of 90 ground motions measured in Iwate-ken, Miyagi-ken, andFukushima-ken during the 2011 Great East Japan earthquake

1359

2.0

1.0

Seismic Intensity Γ =Response Acceleration

P[gi ≤ 0|Γ=γ] of as-built pierP[gi ≤ 0|Γ=γ] of as-built pier

1.0
0.8
0.6

Limit state: g2

0.4

Limit state: g1
Limit state: g3

0.2
0.0

Seismic Intensity Γ =
PGA

0.8
0.6
Limit state: g2

0.4

Limit state: g1
Limit state: g3

0.2
0.0

0

250

500

750

1000

1250

1500

0

200

1.0

Seismic Intensity Γ =Response Acceleration

0.8

Limit state: g4

0.6
0.4

Limit state: g5

0.2
0.0
0

500

1000

1500

2000

2500

400

600

800

1000

PGA (gal)P[gi ≤ 0|Γ=γ] of retrofitted pierP[gi ≤ 0|Γ=γ] of retrofitted pierResponse Acceleration Sa (T1, h) (gal)

3000

1.0

Seismic Intensity Γ =
PGA

0.8

Limit state: g4

0.6
0.4

Limit state: g5

0.2
0.0
0

Response Acceleration Sa (T1, h) (gal)

500

1000

1500

2000

PGA (gal)

Figure 9. Fragility curves of a single-story RC moment-resisting frame pierwith and without a steel jacket
Based on a comparison of experimental results, Tamai et al. (1996) reported that the lateral force
acting on a steel-jacketed RC column decreases sharply beyond the rotation capacity θu,a.
Based on the experimental results of steel-jacketed columns subjected to cyclic loading, Tamai etal. (1998) reported that the hysteretic model of steel-jacketed columns is based on that proposed by
Takeda et al. (1972). In this study, the unloading stiffness kr is given by⎛θ⎞k r = k y ⎜ max ⎟⎜ χ 2θ y′ ⎟
⎝
⎠

−0.5

(10)

where ky is the yielding stiffness and θmax is the maximum curvature attained in the direction ofloading.
The statistics of χ2, χ3, and χ4 can be obtained by comparing the experimental results ofsteel-jacketed RC columns subjected to cyclic loading with computed values. Experimental results
reported by Tamai et al. (1998) are used in this study. The number of specimens used was 12. The
statistics of model uncertainties associated with the evaluation of θ’y,b and θu,b are assumed to be thesame as those associated with the evaluation of θ’y,a and θu,a. Figure 7 shows the comparison ofexperimental and computational results. Because the steel jacket was not anchored to the othercomponents, the ultimate moment Mu of the retrofitted RC columns was calculated by removing theexistence of the steel jacket from consideration. The steel jacket serves to increase the shear strength,
which may affect the flexural strength. The experimental ultimate (=maximum) moments ofsteel-jacketed RC columns are underestimated, as shown in Figure 7. The statistics in Figure 7 are1360

used as the model uncertainties. In addition, the uncertainties associated with material strength areconsidered when My, Mu, θy, and θu are calculated. The parameters associated with material strength
are shown in Akiyama et al. (2010).
Ninety ground motions measured in Iwate-ken, Miyagi-ken, and Fukushima-ken during the 2011
Great East Japan earthquake were used in the nonlinear dynamic analysis performed on the frame pier.
In the MCS, one horizontal component from the ground motion record is randomly selected. The
seismic intensity Γ in the fragility analysis is the PGA or Sa (T1, h), where Sa (T1, h) is the h-damped
spectra acceleration at the fundamental frequency T1 (≈ 0.43 sec) of the analyzed frame pier for theconsidered earthquake record. Each ground motion is amplified such that the PGA or Sa (T1, h) is equal
to a specified seismic intensity. Figure 8 shows the response acceleration of 90 ground motions thatare amplified such that PGA = 1000 gal or Sa (T1, h) = 1000 gal.
Fragility Curves of the As-Built and Retrofitted Shinkansen Viaducts
In the MCS, gi provided by Equations (2) to (6) is calculated by using the maximum value of the peak
shear forces of the RC columns and the ductility demands sustained by the plastic hinges. Figure 9shows the fragility curves illustrating the vulnerability of the as-built and retrofitted frame pier over arange of the seismic intensities PGA or Sa (T1, h).
Because RC columns of the as-built frame pier do not have sufficient shear reinforcement and theshear strength is less than the flexural strength, the fragility curve associated with g1 is located to theleft of that associated with g2. From Figure 3, it might be roughly estimated that the as-built frame pierwas subjected to ground motion with PGA ≈ 200 gal during the 2011 Great East Japan earthquake. If
the frame pier had not been retrofitted, there is a high probability that it would have suffered severe
damage due to shear.
Comparing the fragility curves associated with the limit states g2 and g3 for the as-built frame pierto those associated with g4 and g5 for the retrofitted frame pier, the fragility enhancement is found to be
more significant for the severe-damage state. The physical improvement to seismic vulnerability fromsteel jacketing is evident when enhanced fragility curves are plotted as a function of PGA or Sa (T1, h).
The enhanced curves shift to the right relative to those associated with the frame piers before retrofit.
In 2004, Kim and Shinozuka presented the fragility curve of a typical California-type multiframe
concrete bridge based on a two-dimensional response analysis and an MCS. They developed thefragility curves of a bridge with steel jacketing, indicating the states of damage as none, slight,
moderate, extensive, and complete collapse. It is interesting to note that the fragility curve associatedwith g5 in Figure 9 is similar to the one associated with the extensive damage state presented by Kim
and Shinozuka (2004), even though the bridge types and ground motions used in this and Kim andShinozuka’s studies are different.

CONCLUSIONSThe effectiveness of the seismic retrofit to the Shinkansen viaduct was demonstrated in the 2011 Great
East Japan earthquake. The RC columns retrofitted by means of steel jacketing experienced no damage
during this earthquake. Some of the Shinkansen viaducts were not retrofitted in the first seismic
retrofit program because they were identified as having sufficient shear reinforcement to prevent
brittle failure. They were to be retrofitted in the second seismic retrofit program. Some of the viaductsthat were not retrofitted were severely damaged during the 2011 Great East Japan earthquake. It is
important that rapid progress is made in the seismic retrofit program for the Shinkansen viaducts.
Although the viaduct with retrofitted RC columns sustained no damage during the 2011 Great East
Japan earthquake, it should be noted that the ground motions at the site of the Shinkansen viaducts
induced by the 2011 Great East Japan earthquake were not strong compared with the seismic designforce in the current seismic design code. To evaluate the likelihood of damage of the as-built andretrofitted viaduct over a range of potential earthquake ground motion intensities, seismic fragility
curves were developed. Lognormal distribution functions were derived by a nonlinear dynamic

1361

analysis and an MCS. The simulated fragility curves of the retrofitted viaduct show a great
improvement in seismic performance compared with those of the as-built viaduct.
In this study, the limit states for the viaduct are defined in terms of structural capacities such as
shear strength and rotation ductility. However, the limit states should be provided by considering the
motion performance of Shinkansen and postevent rehabilitation. The investigation of fragility curves
using these limit states is a future challenge.

ACKNOWLEDGMENTS
The first author acknowledges support for this research by the J-RAPID program of the Japan Scienceand Technology Agency (project leader: Prof. Kazuhiko Kawashima, Tokyo Institute of Technology).
We thank the National Research Institute for Earth Science and Disaster Prevention, Japan, forproviding us with strong-motion data recorded by the K-NET.

REFERENCES
Akiyama, M., Matsuzaki, M., Dang, D.H. and Suzuki, M. (2010). “Reliability-based capacity design forreinforced concrete bridge structures.” Structure and Infrastructure Engineering, doi:
10.1080/15732479.2010.507707. (in press)
Japan Society of Civil Engineers. (2004). “Damage analysis of concrete structures due to the earthquakes
in 2003.” Concrete Library, 114. (in Japanese).
Karim, K.R. and Yamazaki, F. (2003). “A simplified method of constructing fragility curves forhighway bridges.” Earthquake Engineering and Structural Dynamics, Vol. 32, 1603-1626.
Kim, S.-H. and Shinozuka, M. (2004). “Development of fragility curves of bridges retrofitted bycolumn jacketing.” Probabilistic Engineering Mechanics, Vol. 19, 105-112.
Kawashima, K. (2000). “Seismic design and retrofit of bridges.” 12th World Conference on
Earthquake Engineering (WCEE), Keynote paper, Auckland, Newzealand.
Kawashima, K., Kosa, K., Takahashi, Y., Akiyama, M., Nishioka T., Watanabe, G., Koga, H. andMatsuzaki, H. (2011). “Damages of Bridges during 2011 Great East Japan Earthquake.” Proceedingof 43rd Joint Meeting, US-Japan Panel on Wind and Seismic Effects, UJNR, Tsukuba Science City,
Japan.
Padgett, J.E. and DesRoches R. (2007a). “Sensitivity of seismic response and fragility to parameter
uncertainty.” Journal of Structural Engineering, Vol. 133, No. 12, 1710-1718.
Padgett, J.E. and DesRoches R. (2007b). “Bridge functionality relationships for improved seismic risk
assessment of transport networks.” Earthquake Spectra, Vol. 23, No.1, 115-130.
Padgett, J.E. and DesRoches R. (2008). “Methodology for the development of analytical fragility
curves for retrofitted bridges.” Earthquake Engineering and Structural Dynamics, Vol. 37,
1157-1174.
Padgett, J.E. and DesRoches R. (2009). “Retrofitted bridge fragility analysis for typical classes ofmultispan bridges.” Earthquake Spectra, Vol. 25, No.1, 117-141.
Shinozuka, M., Feng, M.Q., Lee, J. and Naganuma, T. (2000). “Statistical analysis of fragility curves.”
Journal of Engineering Mechanics, Vol. 126, No. 12, 1224-1231.
Shinozuka, M., Feng, M.Q., Kim, H.-K., Kim, S.-H. (2000). “Nonlinear static procedure for fragility
curve development.” Journal of Engineering Mechanics, Vol. 126, No.12, 1287-1295.
Takeda, T., Sozen, M., Nielse, N. (1970). “Reinforced concrete response to simulated earthquake.”
Journal of Structural Engineering, Vol. 96, No. 12, 2557-2573.
Tamai, S., Takiguchi, M., Hattori, N. (1996). “Ductility capacity of retrofitted RC columns.”
Proceedings of the Japan Concrete Institute, Vol. 20, No. 3, 1111-1116. (in Japanese)
Tamai, S., Tsutomu, S. (1998). “ Ductility of steel jacketed RC columns.” RTRI report, Vol. 12, No. 9,39-44. (in Japanese)1362