Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanDAMAGE ASSESSMENT ON ROAD STRUCTURES
DUE TO SLOPE FAILURES IN THE 2011 OFF
THE PACIFIC COAST OF TOHOKU EARTHQUAKE
Toshiaki SAKURAI1, Gaku SHOJI2, Kazunori TAKAHASHI3 and Tomoharu NAKAMURA4
1

Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba,
Ibaraki, Japan, e0611356@edu.esys.tsukuba.ac.jp
2
Associate Professor, Faculty of Engineering, Information and Systems, University of Tsukuba,
Ibaraki, Japan, gshoji@kz.tsukuba.ac.jp
3
Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba,
Ibaraki, Japan, s1120951@u.tsukuba.ac.jp
4
College of Engineering Systems, University of Tsukuba,
Ibaraki, Japan, e0811237@edu.esys.tsukuba.ac.jp

ABSTRACT: The damage on road structures due to slope failures in the 2011 off the
Pacific Coast of Tohoku earthquake is assessed. We classify 13 types of failure modes for
43 data and analyze them from view of points of dependency of the damage on spatial
distributions of peak ground acceleration, peak ground velocity, and seismic intensity
induced by the earthquake. Previously proposed damage functions on the failures of roadstructures due to slope failures in the 2008 Iwate-Miyagi Nairiku earthquake are verified
by comparing the derived results with the values from the damage functions.
Key Words: The 2011 off the Pacific Coast of Tohoku earthquake, the 2008
Iwate-Miyagi Nairiku earthquake, slope failure, road structure, damage
function

INTRODUCTION
Road structures were damaged severely in the 2011 off the Pacific Coast of Tohoku earthquake(MJMA=9.0) (JMA 2011a) due to not only tsunami waves, but also induced ground excitations. The
ground excitations caused the slope failures in mountainous areas which induce various types ofdamage of road structures. The related researchers and practitioners paid intended attention to thedamage of infrastructures such as road structures due to slope failures during strong ground excitationsin previous extreme earthquakes such as the 2008 Iwate-Miyagi Nairiku earthquake (MJMA=7.2) (Joint
Survey Team of JSCE, JGS, JAEE, and the Japan Landslide Society 2008) and the 2008 Wenchuan
earthquake, China (Mw=7.9) (USGS 2008) (Chigira 2005, Hunag et al. 2007, Nishida et al. 2007,
Fujiwara et al. 2008, Tamakoshi 2008, Kokusho et al. 2009, Konagai et al. 2009, Nishiki et al. 2009,
and Zhang et al. 2009). In these earthquakes, pavement of road structures were suffered and cut slopesof road structures were collapsed due to slope failures by ground shakings. Previous studies wereinvolved in clarifying mechanism of occurrence of slope failures during an earthquake and in961

Table 1 Analyzed data of damaged road structures
Road Management
Sectors

Damage Information(URL)

Road Management
Sectors【Disasiter Prevention Imformation】(Press Release)
Tohoku Regional
Tohoku Regional Development Bureau Earthquake
Development Bureau Imformation (15th Version)
Main Office
http://www.thr.mlit.go.jp/bumon/kisya/saigai/sback/zoku
hou1110.htm

Damage Information(URL)

Kanto Regional
Road Damage Information in the 2011 off the Pacific
Development Bureau
Coast of Tohoku Earthquake (1st and 3rd Versions)Omiya National Road
http://www.ktr.mlit.go.jp/oomiya/04data/kisha/h22.htm
OfficeTohoku Regional
Kanto Regional
Earthquake Imformation : Iwate River and National Road
Damage of National Road No. 298
Development Bureau
Development Bureau
Office (2nd and 3rd Versions)(18:50 on March 11)
Iwate River andShuto National Road
http://www.thr.mlit.go.jp/iwate/bousai/bousai/index.htm
http://www.ktr.mlit.go.jp/syuto/index.htm
National Road Office
OfficeTohoku Regional
Sanriku National Road Office Earthquake Imformation
Development Bureau(2nd Version)
Sanriku National
http://www.thr.mlit.go.jp/sanriku/index.html
Road Office

Kanto Regional
Damage Imformation in the 2011 off the Pacific Coast ofDevelopment Bureau
Tohoku Earthquake (3rd Version)
Yokohama National
http://www.ktr.mlit.go.jp/yokohama/report/bn2010.htm
Road Office【Disasiter Prevention Imformation】
Tohoku Regional(Press Release)
Development Bureau
Sendai River and National Road Office Disaster
Sendai River andInformation (3rd, 13th, and 14th Versions)
National Road Office
http://www.thr.mlit.go.jp/sendai/index.html

Aomori Prefecture

Disaster Countermeasures Office About the Damage inthe 2011 off the Pacific Coast of Tohoku Earthquake(43th Version)
http://www.pref.aomori.lg.jp/【Disasiter Prevention Imformation】 Yamagata River
Tohoku Regionaland National Road Office Earthquake Imformation
Development Bureau(3rd, 4th, 6th, and 7th Versions)
Iwate Prefecture
Yamagata River andhttp://www.thr.mlit.go.jp/bumon/kisya/saigai/sback/zoku
National Road Officehou1106.htm

Situation of Road Traffic Regulation Management due tothe Earthquake in Iwate Prefecture on March 11(As of 9:30 on August 12 )http://www.pref.iwate.jp/list.rbz?nd=2974&ik=1&pnp=2974&of=13【Disasiter Prevention Imformation】Fukushima River andTohoku Regional
National Road Office Earthquake Imformation
Development Bureau
Akita Prefecture(8th Version)
Fukushima River andhttp://www.thr.mlit.go.jp/fukushima/pressedit/disaster_in
National Road Office
dex.html

Imformation Earthquake(2nd, 4th, 5th, 6th, and 9th Versions)
http://www.pref.akita.lg.jp/www/genre/0000000000000/
1243242791775/index.html【Disasiter Prevention Imformation】 Koriyama National
Tohoku Regional
Road Office : Emergency System Response in the 2011
Development Bureau off the Pacific Coast of Tohoku Earthquake
Miyagi Prefecture
Koriyama National(2nd, 8th, and 20th Versions)
Road Office
http://www.thr.mlit.go.jp/bumon/kisya/saigai/sback/zoku
hou1117.htm

Traffic Regulation in the 2011 off the Pacific Coast of
Tohoku Earthquake (As of 16:00 on May 8)
http://www.pref.miyagi.jp/road/kiseinow.htm
Damag of Public Facility and Emergency Disaster
Recovery Situations in the 2011 off the Pacific Coast of
Tohoku Earthquake (Updated August 10)
http://www.pref.miyagi.jp/doboku/110311dbk_taiou/inde
x.htm【Disasiter Prevention Imformation】 Banjyo National
Tohoku Regional(Press Release) The 2011 off the Pacific Coast of Tohoku
Road Office : Road Disasiter Prevention Imformation
Development Bureau
Earthquake (5th Version)
Yamagata Prefecture Earthquake (3rd and 10th Versions)Banjyo National Road
http://www.thr.mlit.go.jp/bumon/kisya/saigai/sback/zoku
http://www.pref.yamagata.jp/
Officehou1132.htm
Road Division at Kanto Regional Development Bureau
Kanto Regional
Disaster Imformation of National Road in the 2011 off
East Nippon
Development Bureau the Pacific Coast of Tohoku Earthquake
Expressway
Main Office(15:00 on March 18, 2011)
Company Limited
http://www.ktr.mlit.go.jp/saigai/kyoku_dis00000021.html

Damaged Routes and Sections (List) (March 18)
http://www.e-nexco.co.jp/whatsnew/h22.html

Hitachi River and National Road Office
Kanto Regional(Press release) : Announcement for the Damage due toDevelopment Bureau
the 2011 off the Pacific Coast of Tohoku Earthquake
Hitachi River and(10:30 on March 12, 2011)
National Road Office
http://www.ktr.mlit.go.jp/kisha/index00000022.html(Press Release) Influence and Emergency Response dueto the 2011 off the Pacific Coast of Tohoku Earthquake
and Correspondence (March 14, 2011)
http://www.shutoko.jp/

Metropolitan
Expressway
Company Limited

Road Damage Information for the 2011 off the Pacific
Kanto Regional
Coast of Tohoku Earthquake
Development Bureau(17:00 on March 11, 18:30 on March 11, 12:00 on
Utsunomiya National
March 12)Road Office
http://www.ktr.mlit.go.jp/utunomiya/bousai/old.htm――

clarifying the dependency of damage of road structures on occurrence of slope failures. Based on
previous valuable results, we analyzed damage data on road structures due to slope failures in the 2011962

Fig. 1 Subject roads without inundation areas
7

Fig. 2 Subject roads for analysis

Frequency

6

A：Road Damage
B：Road Crack
C：Road Gap
D：Road Rupture
E：Road Subsidence
F：Road Collapse

54
3

G：Slope Failure of Embankment
H：Rock Fall
I：Slope Failure
J：Land Slide
K：Land Collapse

L：Combination of Pavement Crack and Slope Failure of Embankment
M：Combination of Pavement Crack and Land Collapse

2
1
0
A

B

C

D

E

Road Failure

F

G

H

I

J

K

L

M

Slope Failure Combination of Road Failure and Slope Failure

Failure modes
Fig. 3 Induced failure modes
off the Pacific Coast of Tohoku earthquake (hereinafter the Tohoku earthquake) and clarified therelationship of related damage ratios with spatial distributions of peak ground acceleration (PGA),
peak ground velocity (PGV), and instrumental seismic intensity (IJ). In addition, damage functions on
the failures of road structures due to slope failures in the 2008 Iwate-Miyagi Nairiku earthquake(hereinafter the Iwate-Miyagi Nairiku earthquake), proposed by Shoji and Sakurai (2011), are verified
by comparing the derived results from this study with the values from the damage functions.

963

SUBJECT ROAD STRUCTURES AND THE DAMAGE MODES
Analyzed data of damaged road structures
Damage data of road structures due to slope failures except damage data of bridges and tunnels areanalyzed. Analyzed road structures are national roads at six prefectures of Tohoku regions, Tokyo
metropolitan areas and six prefectures of Kanto regions by Tohoku Regional Development Bureau,
Kanto Regional Development Bureau, East Nippon Expressway Company Limited and Metropolitan
Expressway Company Limited, and prefectural roads at five prefectures of Tohoku regions without
Fukushima prefecture by local government sectors. Table 1 shows the information of damaged roadstructures which is opened at the related web sites by road management authorities and local
government sectors. Total number of the data is 680. For selecting 680 data, we removed the damage
data to be possibly affected by the ground motions due to the aftershocks after March 11, 2011.
Based on the data, first, we identified the locations of damaged road structures. Second, weremoved 158 data as the data subjected to the tsunami waves by comparing the locations of damaged
road structures with estimated inundation areas by GSI (2011) and selected 522 data as thosedominantly exposed by the ground excitations.
Among 522 data, the exact locations of 360 data offered by East Nippon Expressway Company
Limited cannot be clarified since these data show the number of damage points between any
interchanges. Therefore, we removed above 360 data and set 162 data as analyzed ones. For 162 data,
finally we focused on 43 data which are assumed to be affected by slope failures in subject areas
showing maximum slope gradients equal to or over 10 degrees (Ishide and Yamazaki 2010).
Furthermore, in order to verify validness of occurrence of slope failures and induced damage at subject
road structures, we check all image data for 43 data by Google Earth.
We model subjected roads without estimated inundation areas by GSI as shown in Fig. 1, by using
the digital data of national roads and major prefectural roads in 6 prefectures of Tohoku regions, Tokyo
Metropolitan areas and 6 prefectures of Kanto regions offered by National and Regional Planning
Bureau (2011) and by constructing the digital data of other prefectural roads in 5 prefectures of
Tohoku regions except Fukushima prefecture by checking Google Earth. In addition, among aboveroads, we select the roads with slopes showing maximum slope gradients equal to or over 10 degrees
as shown in Fig. 2. Again we checked the locations of roads with slopes by Google Earth. Total lengthof subject roads is 14,258km.
Damage modes
Fig. 3 shows 13 failure modes: 6 road failure modes, 5 slope failure modes, and 2 combination failuremodes of road failure and slope failure. 25 data on road failure modes are classified into 6 failuremodes: 6 data for road crack, 6 data for road gap, 6 data for road rupture, 4 data for road collapse, andothers. 16 data on slope failure modes are classified into 5 failure modes: 5 data for failure ofembankment slope, 5 data for land collapse, 4 data for rock fall, and others.

DAMAGE ASSESMENT FOR SUBJECT ROAD STRUCTURES
Evaluation of spatial distributions of PGA, PGV, and IJ
Fig. 4 shows estimated spatial distributions with a 250m-mesh of PGA, PGV, and IJ for analysis,
based on the simple kriging method by using 535 observation waveforms by K-NET and KiK-net(NIED 2011), and 44 observation waveforms by JMA (2011b) as shown in Fig. 5. These observatory
stations are distributed at Aomori, Akita, Yamagata, Iwate, Miyagi, Fukushima, Ibaraki, Tochigi,
Gunma, Chiba, Saitama, Yamanashi, Nagano, and Niigata prefectures, and Tokyo Metropolitan areas.
We describe the procedures of computing the distributions of PGA, PGV, and IJ in the followings.

964

(a) PGA distribution(b) PGV distribution(c) IJ distribution
Fig. 4 Spatial distributions of affected roads and PGA, PGV, and IJ

965

Fig. 5 Observatory stations for analysis
First, PGA at an arbitrary station is computed by selecting maximum value in a time history
composing EW, NS, and UD components of an observed waveform. We calibrate the time history databy subducting mean value from the data recorded by K-NET and KiK-net. We compute PGAb600 at abase level with average S wave velocity Vs of 600m/s by applying the related factors α, β on
amplification of PGA at a ground surface compared with PGAb600. The amplification factors α, β are
obtained by the following equations proposed by Suetomi et al. (2005),

XS =α ⋅ Xb
X S = X L − β ⋅ (X b − X 2 )2
X2 = XL − X(X b ≤ X 1 )(X 1 < X b < X 2 )
(1)

α

β=

X L − α ⋅ X1

( X 2 − X 1 )2

XS = XL
log(α ) = 2.024 − 0.75 ⋅ log( AVS 20)
log( X 1 ) = 1.4 ⋅ log( AVS 20) − 0.8log( X L ) = 1.0 ⋅ log( AVS 20) + 0.778(X b ≥ X 2 )
(2)
(3)
(4)

Now, in Eq. (1) to Eq. (4), we set XS=PGA and Xb=PGAb600, and interpret X1 and X2 as the thresholdvalues describing the relation between XS and Xb dependent on classification of subject groundcondition. AVS20 is an average S wave velocity at a layer of 20m under a ground surface, andcomputed by the following equation proposed by Kanno et al. (2006),

966

AVS 30 = 1.13 AVS 20 + 19.5

(5)

where AVS30 is similarly average S wave velocity at a layer of 30m under a ground surface, and we
obtain the value with a 250m-mesh from the data of geomorphologic classification (Matsuoka et al.
2005). By using estimated PGAb600 data at observatory stations, we compute PGAb600 with a
250m-mesh based on simple kriging interpolation. We use attenuation relationship between PGAb600
and minimum distance from an arbitrary site to a fault plate R proposed by Shi and Midorikawa (1999),
for evaluating the mean trend component in adopting simple kriging method as shown in the following
equation,

Log10 PGAb 600 = c1 − Log10 (R + c2 ) + c3

(6)

where c1, c2, and c3 are recurrence constants obtained by the least squares method. In addition, forevaluating the variance in adopting simple kriging method, we use exponential model as a covariancemodel,

γ = Var[ PGAb 600 2 ] exp (−h a )(7)where γ is the covariance of PGAb600, h is the distance between an arbitrary site with a 250m-mesh andthe observatory station, and a is the correlation distance. We set a=40km for which the variation of
spatial distributions of PGA converges when a varies for 20km, 30km, 40km, and 50km.
PGV at an arbitrary station is computed by selecting maximum value in a time history composing
two horizontal EW and NS components of an observed waveform integrated by acceleration EW andNS waveforms with filtering by Bata Worth high pass filter with lowest cut-off frequency of 0.05Hz
and pass frequency of 0.1Hz for K-NET and KiK-net waveforms, and with filtering of cut-off
frequency equal to or less than 0.2Hz by using the integration recurrence formula for JMA waveforms.
We compute PGVb600 at a base level with average S wave velocity Vs of 600m/s by applying therelated factor ARV on amplification of PGV at a ground surface compared with PGVb600. The relationof PGVb600 with PGV is obtained by the following equations proposed by Fujimoto and Midorikawa(2006),

PGVb 600 = PGV ARV(8)

Log10 ARV = 2.367 − 0.852 Log10 AVS 30(9)

By using estimated PGVb600 data at observatory stations, we compute PGVb600 with a 250m-meshbased on simple kriging interpolation. We use attenuation relationship between PGVb600 and R
proposed by Shi and Midorkawa (1999), for evaluating the mean trend component in adopting Simple
Kriging method as well as for computation of PGA. In addition, for evaluating the variance inadopting simple kriging method, we use exponential model as a covariance model. We set a=40km forwhich the variation of spatial distribution of PGV converges when a varies for 20km, 30km, 40km,
and 50km.
IJ at an arbitrary station is computed by computational scheme by JMA (2011c). We compute
IJb600 at a base level with average S wave velocity Vs of 600m/s by applying the related factors α, β on
amplification of IJ at a ground surface compared with IJb600. The amplification factors α, β are
obtained by the following equations proposed by Suetomi et al. (2005),

967

λIJ = α IJ
λIJ = α IJ − β ⋅ (IJ b − IJ 1 )α − IJ L + IJ 2
β IJ = IJ

IJ 2 − IJ 1
λ IJ = IJ L − IJ b

α IJ = 2.699 − log( AVS 20 )IJ 1 = 0.8 + 2.25 ⋅ log( AVS 20)
IJ 2 = 1.15 + 2.4 ⋅ log( AVS 20)
IJ L = 2.2 + 2.0 ⋅ log( AVS 20)(IJ b ≤ IJ1 )(IJ1 < IJ b < IJ 2 )(10)(IJ 2 ≤ IJ b )
(11)
(12)
(13)
(14)

By using estimated IJb600 data at observatory stations, we compute IJb600 with a 250m-mesh based on
simple kriging interpolation. We apply same procedures for evaluating the mean trend component andvariance in adopting simple kriging method, and for setting the correlation distance a as well as theprocedures for computation of spatial distributions of PGA and PGV.
We verify the derived spatial distributions of PGA, PGV, and IJ from above procedures with same
spatial distributions computed by NIED (2011), JMA (2011a), Suetomi and Fukushima (2011), andAIST (2011), and we check the agreement of our results with the reference results.
Relations of damage ratio with PGA, PGV, and IJ
Fig. 6 shows the relations between road damage and spatial distributions of PGA, PGV, and IJ. Now,
we define damage ratio R as the ratio of the number of damage points X divided by total exposed road
lengths L in an unit of kilometer. For damage ratio R with PGA of 0m/s2 to 20m/s2, the interval of PGA
is set as 0.5m/s2, for R with PGV of 0.01m/s to 1.4m/s, the interval of PGV is set as 0.01m/s, and for R
with IJ of 2.5 to 6.7, the interval of IJ is set as 0.1.
From Fig. 6(a), R with PGA of 0.5m/s2 shows the minimum value of 0.000264/km at the lowest
limit of PGA and R with PGA of 11.5m/s2 shows the maximum value of 0.0589/km. R with PGA of
1.5m/s2 to 3.0m/s2 increases the value of 0.000637/km to 0.00333/km, R with PGA of 3.0m/s2 to
7.0m/s2 increases the value of 0.00264/km to 0.0316/km, and R with PGA of 9.0m/s2 to 11.5m/s2
increases the value of 0.0229/km to 0.0589/km. In contrast, R with PGA over 12m/s2 shows zero inspite of becoming higher PGA. This is because the possibility of occurrence of road damage becomes
low with shortening exposed road lengths less than 17.7km.
From Fig. 6(b), R with PGV of 0.1m/s shows the minimum value of 0.00239/km at the lowest
limit of PGV and R with PGV of 0.62m/s shows the maximum value of 0.0687/km. R with PGV of
0.1m/s to 0.3m/s increases the value of 0.00239/km to 0.0202/km, R with PGV of 0.3m/s to 0.5m/s
increases the value of 0.00964/km to 0.0508/km, and R with PGV of 0.5m/s to 0.62m/s increases thevalue of 0.0312/km to 0.0687/km. R with PGV over 0.63m/s shows zero in spite of becoming higher
PGV, that is caused by same reason for higher PGA over 12m/s2.
From Fig. 6(c), R with IJ of 3.7 shows the lower value of 0.00169/km at the lowest limit of IJ and
R with IJ of 5.9 shows the maximum value of 0.0226/km. R with IJ of 4.5 to 5.0 increases the value of0.00176/km to 0.00401/km, R with IJ of 5.0 to 5.5 increases the value of 0.00157/km to 0.0139/km,
and R with IJ of 5.5 to 5.9 increases the value of 0.00690/km to 0.0226/km. Similarly, R with IJ over
6.0 shows zero in spite of becoming higher IJ.
Comparison of analyzed data with previous damage functions
Fig. 7 shows the comparison of analyzed data for the Tohoku earthquake with damage ratios for the
Iwate-Miyagi Nairiku earthquake data and damage functions by the Iwate-Miyagi Nairiku earthquake
data proposed by Shoji and Sakurai (2011).

968

0.07

0.06

0.06

Damage Ratio R

Damage Ratio R

0.07

0.05
0.04
0.03
0.02
0.01

0.05
0.04
0.03
0.02
0.01

0

0

0

5

10
PGA(m/s2)

15

20

0

0.2

0.4

(a) For PGA

0.6 0.8
PGV(m/s)

1

1.2

1.4

(b) For PGV

0.025

Damage Ratio R

0.02
0.015
0.01

0.005
0
2.5

3

3.5

4

4.5 5
IJ

5.5

6

6.5

7

(c) For IJ
Fig. 7 Comparison of the damage ratio for PGA, PGV, and IJ
From Fig. 7(a), averaged values of difference from observed data for the Iwate-Miyagi Nairiku
earthquake to analyzed data for the Tohoku earthquake with PGA of 3.0m/s2 to 6.0m/s2 shows
0.038/km and those with PGA of 6.0m/s2 to 10m/s2 at higher PGA becomes the larger value of
0.13/km. Averaged values of difference from the values by damage function to analyzed data for the
Tohoku earthquake with PGA of 3.0m/s2 to 6.0m/s2 shows 0.036/km and those with PGA of 6.0m/s2 to
10m/s2 at higher PGA shows the larger value of 0.18/km. In the above, R with relatively lower PGA of
3.0m/s2 to 6.0m/s2 shows the narrow differences. In contrast, R with relatively higher PGA of 6.0m/s2
to 10m/s2 shows the wider differences.
From Fig. 7(b), averaged values of difference from observed data for the Iwate-Miyagi Nairiku
earthquake to analyzed data for the Tohoku earthquake with PGV of 0.1m/s to 0.3m/s shows 0.052/km
and those with PGV of 0.5m/s to 0.6m/s shows the larger value of 0.22/km. Averaged values ofdifference from the values by damage function to analyzed data for the Tohoku earthquake with PGVof 0.1m/s to 0.3m/s shows 0.0043/km and those with PGV of 0.5m/s to 0.6m/s shows the larger of
0.17/km. In the above, R with relatively lower PGV of 0.1m/s to 0.3m/s shows the narrow differences.
In contrast, R with relatively higher PGV of 0.5m/s to 0.6m/s shows the larger wider differences.
From Fig. 7(c), averaged values of difference from observed data for the Iwate-Miyagi Nairiku
earthquake to analyzed data for the Tohoku earthquake with IJ of 4.5 to 5.5 shows 0.024/km and thosewith IJ of 5.5 to 6.5 shows the larger value of 0.26/km. Averaged values of difference from the values
by damage function to analyzed data for the Tohoku earthquake with IJ of 4.5 to 5.5 shows 0.017/km
and those with IJ of 5.5 to 6.5 shows the larger value of 0.29/km. In the above, R with relatively lower
IJ of 4.5 to 5.5 shows the narrow differences. In contrast, R with relatively higher IJ of 4.5 to 5.5
shows the larger wider differences.

969

1.6

Damage ratio for the Iwate-Miyagi
Nairiku earthquake
Damage function for the Iwate-Miyagi
Nairiku earthquake
Damage ratio for the Tohoku earthquake

1.2

0.6

Damage Ratio R

Damage Ratio R

1.4

Damage ratio for the IwateMiyagi Nairiku earthquake
Damage function for the IwateMiyagi Nairiku earthquake
Damage ratio for the Tohoku
earthquake

0.7

1
0.8
0.6
0.4

0.5
0.4
0.3
0.2
0.1

0.2
0

0
0

5

10

15
20
25
PGA(m/s2)

30

35

0

0.2

0.4

(a) For PGA

0.6 0.8
PGV(m/s)

1

1.2

1.4

(b) For PGV

0.6

Damage ratio for the Iwate-Miyagi
Nairiku earthquake
Damage function for the Iwate-Miyagi
Nairiku earthquake
Damage ratio for the Tohoku
earthquake

0.5

Damage Ratio R

0.4
0.3
0.2
0.1
0
2.5

3

3.5

4

4.5 5
IJ

5.5

6

6.5

7

(c) For IJ
Fig. 6 Comparison of analyzed data for the Tohoku earthquake with damage ratios for the
Iwate-Miyagi Nairiku earthquake data and damage functions by the Iwate-Miyagi Nairiku
earthquake data
Hence, ground excitations with PGA of 6.0m/s2 to 10m/s2, PGV of 0.5m/s to 0.6m/s, and IJ of 4.5
to 5.5 for the Iwate-Miyagi Nairiku earthquake induced larger damage of road structures due to slope
failures than those with same ranges of PGA, PGV, and IJ for the Tohoku earthquake.
CONCLUSIONSWe analyzed damage data on road structures due to slope failures in the 2011 off the Pacific Coast of
Tohoku earthquake and clarified the relationship of related damage ratios with spatial distributions ofpeak ground acceleration (PGA), peak ground velocity (PGV), and instrumental seismic intensity (IJ).
In addition, previously proposed damage functions on the failures of road structures due to slope
failures in the 2008 Iwate-Miyagi Nairiku earthquake are verified by comparing the derived resultsfrom this study with the values from the damage functions.
(1) The failure modes are classified for 43 data on the damage of road structures due to slope failures
into 13 failure modes: 6 road failure modes, 5 slope failure modes, and 2 combination failuremodes of road failure and slope failure. 25 data on road failure modes are classified into 6 failuremodes: 6 data for road crack, 6 data for road gap, 6 data for road rupture, 4 data for road collapse,
and others. 16 data on slope failure modes are classified into 5 failure modes: 5 data for failures ofembankment slope, 5 data for land collapse, 4 data for rock fall, and others.
(2) Damage ratio R was defined as the ratio of the number of damage points X divided by total
exposed road lengths L in an unit of kilometer. R with PGA of 0.5m/s2 shows the minimum valueof 0.000264/km at the lowest limit of PGA and R with PGA of 11.5m/s2 shows the maximum value970

of 0.0589/km. R with PGV of 0.1m/s shows the minimum value of 0.00239/km at the lowest limitof PGV and R with PGV of 0.62m/s shows the maximum value of 0.0687/km. R with IJ of 3.7
shows the lower value of 0.00169/km at the lowest limit of IJ and R with IJ of 5.9 shows the
maximum value of 0.0226/km.
(3) Ground excitations with PGA of 6.0m/s2 to 10m/s2, PGV of 0.5m/s to 0.6m/s, and IJ of 4.5 to 5.5
for the Iwate-Miyagi Nairiku earthquake induced larger damage of road structures due to slope
failures than those with same ranges of PGA, PGV, and IJ for the Tohoku earthquake.

ACKNOWLEDGMENTS
We appreciate valuable supports for modeling of damage functions from Professor Yamada Y. andProfessor Matsushima T. at University of Tsukuba, and also appreciate valuable cooperation for
calculating of spatial distributions of PGA, PGV, and IJ from Mr. Kado S. and Mr. Hang Q. at
University of Tsukuba.
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