Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanDAMAGE ASSESSMENT ON ELECTRIC POWER
FAILURES DURING THE 2011 OFF THE PACIFIC
COAST OF TOHOKU EARTHQUAKE
Gaku SHOJI1, Dai TAKAHASHI2, Takuya TSUKIJI3 and Satoshi NABA4
1

Associate Professor, Faculty of Engineering, Information and Systems, University of Tsukuba,
Ibaraki, Japan, gshoji@kz.tsukuba.ac.jp
2
Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba,
Ibaraki, Japan, s1020985@u.tsukuba.ac.jp
3
College of Engineering Systems, University of Tsukuba, Ibaraki, Japan,
e0811228@edu.esys.tsukuba.ac.jp
4
Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba,
Ibaraki, Japan, s1021001@u.tsukuba.ac.jp

ABSTRACT: We collected the data by surveying the related web sites on power failuresduring the 2011 off the Pacific Coast of Tohoku earthquake for Kanto areas, and byinterviewing to the local government sectors and TEPCO branch offices. We quantify
two damage ratios on power failures for subject cities and towns defined by the ratio of
the number of affected households and houses at a city by the number of the relatedhouseholds and houses. The dependency of the damage ratios on induced seismic
intensities is revealed. The related damage functions with power failures are developed.
Key Words: The 2011 off the Pacific Coast of Tohoku earthquake, electric power failure,damage ratio, damage function

INTRODUCTION
The 2011 off the Pacific Coast of Tohoku earthquake caused severe damage on lifeline systems suchas water treatments, energy supply systems, communication networks and transportation facilities.
Among them, electric power failures occur at maximumly 4,858,580 houses in the areas offered by
Tohoku Electric Power Company as of March 17, 2011 (Tohoku Electric Power Company, Inc. 2011)
and at maximumly 4,050,000 houses in the areas offered by Tokyo Electric Power Company as ofMarch 11, 2011 (Tokyo Electric Power Company, Inc. 2011). In the past severe earthquakes, electric
power failures occurred: at maximumly 1,600,000 houses in the 1995 Kobe earthquake (Editorial
Committee for the Report on the Hanshin-Awaji Earthquake Disaster 1997), at maximumly 280,000
houses in the 2004 Niigata-ken Chuetsu earthquake (Hashimoto 2004), at maximumly 35,344 housesin the 2007 Niigata-ken Chuetsu-oki earthquake (Cabinet Office, Government of Japan 2007), and at
29,320 houses in the 2008 Iwate-Miyagi earthquake (Joint Research Committee of Four Societies in
Tohoku Regions on the Iwate-Miyagi Earthquake 2009). The damage assessment for these power
failures is significant to implement the associated data for risk assessment on power failures1552

141°0'0"E

Ibaraki: 32 cities, 10 towns and 2 villages
Tochigi: 14 cities and 12 towns
Chiba: 36 cities, 17 towns,1 village and 6 wards
Saitama: 39 cities, 23 towns,1 village and 10 wards
Tokyo: 25 cities, 2 towns,1village and 23 wards
Kanagawa:19 cities,13 towns, 1 village and 28 wards

Tochigi
prefecture
Saitamaprefecture

Ibarakiprefecture

36°0'0"N

36°0'0"N

37°0'0"N

140°0'0"E

37°0'0"N

Seismicintensity
intensity139°0'0"E
IJ
Seismic
IJ(2.5-3.5](3.5-4.5](4.5-5.0](5.0-5.5](5.5-6.0](6.0-6.5](6.5-6.9]

Tokyo
Metropolitan areas

Kanagawa
prefecture
139°0'0"E

140°0'0"E

35°0'0"N

35°0'0"N

Chiba
prefecture

141°0'0"E

Fig. 1 Subject cities and towns, and spatial distribution of seismic intensity IJ
and induced consequences at a hazardous region for the future disaster prevention. From the reason
above, we analyze damage on electric power failures during the 2011 off the Pacific Coast of Tohoku
earthquake for cities and towns at Ibaraki, Tochigi, Chiba, Saitama and Kanagawa prefectures andTokyo Metropolitan areas.

METHOD OF THE SURVEY
We survey the related web sites on power failures during the 2011 off the Pacific Coast of Tohoku
earthquake for cities and towns at Ibaraki, Tochigi, Chiba, Saitama and Kanagawa prefectures andTokyo Metropolitan areas, and we interview to the local government sectors and TEPCO branch
offices. The total number of subject cities and towns is 315: 32 cities, 10 towns, and 2 villages at
Ibaraki, 14 cities and 12 towns at Tochigi, 36 cities, 17 towns, 1 village and 6 wards at Chiba, 39 cities,
23 towns, 1 village and 10 wards at Saitama, 25 cities, 2 towns, 1 village and 23 wards at Tokyo
Metropolitan areas, 19 cities, 13 towns, 1 village and 28 wards at Kanagawa as shown in Fig. 1.
INDICES FOR THE ANALYSIS
Based on collected data, we analyze whether power failures occurred or not, the number of households
and houses affected by power failures at a city i NPFi and the restoration periods DRP. We quantify the
relative frequency f RPF defined as the ratio of the number of affected cities and towns divided by total
number of subject cities and towns at a same class for seismic intensity IJ. In addition, we quantify
two damage ratios Rhi and Rci at a city i, defined as the ratio of the number of affected households andhouses NPFi divided by the number of households Nhi and houses Nci as the following equations,

Rih =

N iPF
N ih

(1)

Ric =

N iPF
Nic

(2)

1553

Relative frequency f RPF

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Without power
failures
With power
failures

Seismic intensity IJ

Fig. 2 Relation of relative frequency f RPF with seismic intensity IJ
Table 1 Frequency of affected cities and towns by power failures with seismic intensity IJ andcumulative probability Pf of occurrence of power failures with IJ
Seismic
intensity
IJ

Frequency
With power failures

Cumulative probability Pf ofoccurrence of power failures

3.5～4.4
4.5～4.9
5.0～5.4
5.5～5.9
6.0～6.4

Cumulative probability

Without power failures

With power failures

19

10

0.34

40
42
6
0

29
70
44
37

0.42
0.63
0.88
1.00

6.5～

0

5

Summation

107

195

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Data with power
failures
Damage function

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
Seismic intensity IJ

1.00-

Table 2 Identified parameters of damage
function on occurrence of power
failures
Inclination
4.09
Intercept-6.22
Coefficient of determination
0.83
Parameter λ1.52
Parameter ζ
0.24
Mean µ x
4.72Standard deviation σx
1.38~
Median mx
4.58

Fig. 3 Damage function on occurrence of power
failuresDAMAGE ASSESSMENT ON POWER FAILURES
Analysis on occurrence of power failures
Fig. 2 shows the relation of relative frequency f RPF with seismic intensity IJ. Now, we use median of1554

Affected households

60,00050,00040,00030,00020,00010,0000Affected houses

IJ (median)Accurate number
Approximate number
Without power failures
IJ(maximum)
IJ (maximum)
Accurate number
Approximate number
Without power failures

160,000
140,000
120,000
100,000
80,00060,00040,00020,0000

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Seismic intensity IJ

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Seismic intensity IJ(a) Affected households(b) Affected houses
Fig. 4 Relation of the number of affected households and houses NPFi at a city i with seismic intensity
IJ
Number of affected

36°0'0"N

36°0'0"N

35°0'0"N

35°0'0"N

36°0'0"N
35°0'0"N

140°0'0"E

141°0'0"E

139°0'0"E

140°0'0"E

Numberhouses of affected houses
141°0'0"E

No
NoInformation
information
Without
Without
power
power
failuresfailures1-2000
1-2,000
2001-5000
2,001-5,000
5,001-10,000
5001-10000
10,001-20,000
10001-20000
20,001-50,000
20001-50000
50,001-100,000
50001-100000
100001100,00137°0'0"N

139°0'0"E

36°0'0"NNo
No information
information
without power
failuresWithout
power
failures1-10000
1-10,000
10001-20000
10,001-20,000
20001-30000
20,001-30,000
30001-50000
30,001-50,000
5000150,001-

35°0'0"N

140°0'0"E

141°0'0"E

37°0'0"N

139°0'0"E

Number of affected

Numberof affected households
households
37°0'0"N

140°0'0"E

37°0'0"N

139°0'0"E

141°0'0"E(a) Affected households(b) Affected houses
Fig. 5 Spatial distribution on the number of affected households and houses NPFi
seismic intensity IJ for a city i. f RPF shows 0.33 at IJ of 3.0 - 3.1. f RPF increases to 0.50 - 0.60 at IJ of
3.2 to 5.1 although f RPF shows zero at IJ of 3.2-3.3, 0.33 at IJ of 3.6 - 3.7 and 0.44 at IJ of 4.0 - 4.1.
f RPF increases to 0.78 - 1.00 at IJ of 5.2 to 6.1.
Table 1 shows the frequency of affected cities and towns by power failures with seismic intensity
IJ and cumulative probability Pf of occurrence of power failures with IJ. Based on the data, we derive
the damage function idealized by logarithmic distribution as shown in the following equation,x

Pf = ∫0 1  ln x − λ 1dxexp− 2π ⋅ ζ ⋅ x 2 ζ

(3)

where λ and ζ are parameters describing logarithmic distribution. Random variable X is a seismic
intensity IJ. Fig. 3 shows the derived damage function and Table 2 shows the related parameters.
Analysis on the number of affected households and houses
Fig. 4 shows the relation of the number of affected households and houses NPFi at a city i with seismic
intensity IJ. In analyzing the data, we use median and maximum values of seismic intensity IJ for acity i. From Fig. 4(a), we select most influenced city and ward for each prefecture: 27,291 households
at Moka city (IJ=5.2) in Tochigi prefecture, 43,406 households at Kounosu city (IJ=5.1) in Saitama1555

140°0'0"E

35°0'0"N

36°0'0"N

37°0'0"N

139°0'0"E

141°0'0"E

35°0'0"N

36°0'0"N
35°0'0"N

36°0'0"N
35°0'0"N

140°0'0"E

37°0'0"N

140°0'0"E

139°0'0"E

Damage ratio
Damageratio RicNo
Noinformation
information
Without
power
failuresfailures
Without
power
0.0-0.1
0.0-0.1
0.1-0.2
0.1-0.2
0.2-0.3
0.2-0.3
0.3-0.4
0.3-0.4
0.4-0.5
0.4-0.5
0.5-0.6
0.5-0.6
0.6-0.7
0.6-0.7
0.7-0.8
0.7-0.8
0.8-0.9
0.8-0.9
0.9-1.0
0.9-1.036°0'0"N

139°0'0"E

141°0'0"E

37°0'0"N

140°0'0"E

37°0'0"N

139°0'0"E

Damage ratio
Damageratio RihNo
Noinformation
information
Without
power
failuresfailures
Without
power
0.0-0.1
0.0-0.1
0.1-0.2
0.1-0.2
0.2-0.3
0.2-0.3
0.3-0.4
0.3-0.4
0.4-0.5
0.4-0.5
0.5-0.6
0.5-0.6
0.6-0.7
0.6-0.7
0.7-0.8
0.7-0.8
0.8-0.9
0.8-0.9
0.9-1.0
0.9-1.0

141°0'0"E

141°0'0"E(a) Damage ratio Rhi(b) Damage ratio Rci
Fig. 6 Spatial distribution on the damage ratio Rhi and Rci
h

c

0
6.0

Damage ratio Ri0
0.0-0.1
0.1-0.2 0.2-0.3
0.3-0.4 0.4-0.5
0.5-0.6 0.6-0.7
0.7-0.8 0.8-0.9
0.9-1.0128
40
3.0 3.6
4.2 4.8
5.4

0.9-1.0
0.7-0.8
0.5-0.6
0.3-0.4
0.1-0.2

Frequency

0.9-1.0
0.7-0.8
0.5-0.6
0.3-0.4
0.1-0.2

Frequency

Damage ratio Ri0
0.0-0.1
0.1-0.2 0.2-0.3
0.3-0.4 0.4-0.5
0.5-0.6 0.6-0.7
0.7-0.8 0.8-0.9
0.9-1.0128
40
3.0 3.6
4.2 4.8
5.40
6.0(a) Frequency on Rhi(b) Frequency on Rci
hcFig. 7 Frequency of damage ratios R i and R i with seismic intensity IJ
prefecture and 55,700 households at Midori ward (IJ=4.7) in Yokohama city. From Fig. 4(b), we selectmost influenced city for each prefecture: 151,517 houses at Mito city (IJ=5.7) in Ibaraki prefecture,
134,000houses at Utsunomiya city (IJ=5.2) in Tochigi prefecture, 47,000 houses at Gyoda city
(IJ=5.2) in Saitama prefecture, 36,567 houses at Katori city (IJ=5.2) in Chiba prefecture, 106,400
houses at Machida city (IJ=4.3) in Tokyo Metropolitan areas and 133,037 houses at Yokosuka city
(IJ=4.0) in Kanagawa prefecture.
Fig. 5 shows spatial distribution on the number of affected households and houses NPFi. From Fig.
5(a), NPFi for Midori ward and Sakae ward at Yokohama city show larger values over 50,000
households. From Fig. 5(b), NPFi for 12 cities and towns at Ibaraki prefecture and 7 cities and towns at
Tochigi prefecture show larger values over 20,000 houses. NPFi for 2 cities at Saitama prefecture and 3
cities and towns at Chiba prefecture also show larger values over 20,000 houses. NPFi for the boundary
regions between Tokyo metropolitan areas and Kanagawa show over 100,000 houses.
Fig. 6 shows spatial distribution on the damage ratios Rhi and Rci. From Fig. 6(a), Rhi for easternareas in Tochigi prefecture show higher values over 0.9. Rhi for western areas in Saitama prefecture
show higher values over 0.7. Rhi for Midori ward and Sakae ward in Yokohama city show higher
values over 0.7. From Fig. 6(b), Rci for 21 cities and towns in Ibaraki prefecture and 12 cities andtowns at Chiba prefecture show higher values over 0.6.
Fig. 7 shows frequency of damage ratios Rhi and Rci with seismic intensity IJ. We use median ofseismic intensity IJ. From Fig. 7(a), frequency of Rhi of 0.0 to 0.4 becomes high at IJ of 3.0 to 4.5
whereas frequency of Rhi of 0.7 to 0.8 becomes low at the same range of IJ. Frequency of Rhi over 0.8
becomes high at IJ over 4.7. From Fig. 7(b), frequency of Rci of 0.0 to 0.6 becomes high at IJ of 3.0 to

1556

Restoration periods(day)6

141°0'0"E

139°0'0"E

140°0'0"E

141°0'0"E

37°0'0"N7

Without the
information of timeand second

536°0'0"N

36°0'0"N

4
3

No information
Without power failures
0-1
1-2
2-3
3-4
4-5
5-

140°0'0"E

37°0'0"N

With the informationof time and second

139°0'0"E

2

0
3.0

3.5

4.0

4.5 5.0 5.5 6.0
Seismic intensity IJ

6.5

Fig. 8 Relation of the restoration periods DRP

7.0

35°0'0"N1
35°0'0"N

Restoration period(day) DRP

8

Fig. 9 Spatial distribution on restoration
periods DRP with seismic intensity IJ

Table 3 Frequency of affected cities and towns for restoration periods DRP with seismic intensity IJ andcumulative probabilities on restoration periods DRP with IJ
Restoration
Frequency(Seismic intensity IJ)
Cumulative probability
period DRP
IJ=7 IJ=6 higher IJ=6 lower IJ=5 higher ≤ IJ=4.9 ≥ IJ=6.5 ≥ IJ=6.0 ≥ IJ=5.5 ≥ IJ=5.0(days)
0～0.25
0
0
8
42
59
0.00
0.00
0.07
0.46
0.25～0.5
0
1
7
19
16
0.00
0.02
0.19
0.63
0.51～1.0
0
3
12
0
1
0.00
0.19
0.94
0.94
1.01～1.5
1
2
4
4
0
0.09
0.27
0.64
1.00
1.51～2.0
0
6
10
4
0
0.00
0.30
0.80
1.00
2.01～2.5
0
1
0
0
0
0.00
1.00
1.00
1.00
2.51～3.0
0
10
1
0
0
0.00
0.91
1.00
1.00
3.01～3.5
0
0
0
0
0 －
－
－
－
3.51～4.0
0
7
3
0
0
0.00
0.70
1.00
1.00
4.01～4.5
0
0
0
0
0 －
－
－
－
0
0.67
0.83
1.00
1.00
4.51～5.0
41
10
5.01～5.5
0
0
0
0
0 －
－
－
－
5.51～6.0
0
2
0
0
0
0.00
1.00
1.00
1.00
6.01～6.5
0
0
0
0
0 －
－
－
－
6.51～7.0
0
1
0
0
0
0.00
1.00
1.00
1.00
Summation
5
34
46
69
76 －
－
－
－

4.7 whereas frequency of Rci of 0.6 to 0.9 becomes low at the same range of IJ. Frequency of Rci over
0.6 becomes high at IJ over 4.8
Analysis on the restoration periods DRP
Fig. 8 shows relation of the restoration periods DRP with seismic intensity IJ. Fig. 9 shows spatial
distribution on the restoration periods DRP. We use median of seismic intensity IJ. From Fig. 8, DRP for
cities and towns at IJ of 3.0 to 4.5 show 0.3 days to 0.7 days, that is nearly half a day. DRP for
Funabashi city and Sakura city in Chiba at IJ over 4.5 show 1 day, DRP for Oamishirosato town in
Chiba at IJ of 4.7 shows 2 days and DRP for Daigo town in Tochigi at IJ of 5.0 shows 5 days. Moreover,
we select most influenced city and town for each prefecture: 7 days at Kashima city (IJ=5.8) in Ibaraki,
4 days at Mogi town (IJ=5.8) in Tochigi, 0.6 days at Kounosu city (IJ=5.2) in Saitama, 3 days at1557

Table 4 Identified parameters of damage
function on restoration periods
DRP with seismic intensity IJ

Cumulative probability Pf
on restoration periods DRP

Data≥ IJ=6.5≥ IJ=6.0
震度6弱以上≥ IJ=5.5
震度5強≥ IJ=5.0
震度7

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

震度6強以上≥ IJ=6.5 ≥ IJ=6.0 ≥ IJ=5.5 ≥ IJ=5.0

Damage function
震度7≥ IJ=6.5
震度6強≥ IJ=6.0
震度6弱≥ IJ=5.5
震度5強≥ IJ=5.0

01

2 3 4 5 6 7 8 9 10
Restoration periods DRP(days)

Inclination
Intercept
Coefficient ofdetermination
Parameter λParameter ζMean µx

1.47
-1.94

1.33
-1.01

1.20
0.31

1.18
1.40

1.00

0.86

0.42

1.00

1.32
0.68
4.70

0.76
0.75
2.85

-0.26
0.83
1.09

-1.19
0.85
0.44

Standard
deviation σx

13.02

6.22

1.19

0.20

~
Median m
x

3.73

2.15

0.77

0.30

Fig. 10 Damage function on restoration periods
DRP with seismic intensity IJ
Katori city (IJ=5.2) in Chiba, 0.5 days at Machida city (IJ=4.3) in Tokyo Metropolitan areas, 2 days at
Miura city (IJ=4.1), Kamakura city (IJ=3.7), Hayama town (IJ=3.7) and Hiratsuka city (IJ=4.7) in
Kanagawa.
From Fig. 9, DRP for northern areas and coastal areas at Ibaraki prefecture show over 4 days which
is longer than other areas. On the other hand, DRP for the areas at Saitama prefecture and Kanagawa
prefecture show within 1 day which is relatively shorter.
Table 3 shows the frequency of affected cities and towns for restoration periods DRP with seismic
intensity IJ and cumulative probabilities on restoration periods DRP with IJ. As well as the damage
function on occurrence of power failures in Fig. 3, we derive the damage function on restoration
periods DRP with seismic intensity IJ idealized by same model as Eq. (3). Fig. 10 shows the derived
damage function and Table 4 shows the related parameters.

CONCLUSIONS
We surveyed the related web sites on power failures during the 2011 off the Pacific Coast of Tohoku
earthquake for cities and towns at Ibaraki, Tochigi, Chiba, Saitama and Kanagawa prefectures andTokyo Metropolitan areas, and we interviewed to the local government sectors and TEPCO branch
offices. Based on the data, we quantified the relative frequency f RPF defined as the ratio of the number
of affected cities and towns divided by the total number of subject cities and towns for seismic
intensity IJ. In addition, we quantify two damage ratios Rhi and Rci at a city i, defined as the ratio of thenumber of affected households and houses NPFi divided by the number of households Nhi and houses
Nci. The following conclusions are deduced.
1) Relative frequency f RPF shows 0.33 at IJ of 3.0-3.1. f RPF increases to 0.50-0.60 at IJ of 3.2 to 5.1
although f RPF shows zero at IJ of 3.2-3.3, 0.33 at IJ of 3.6-3.7 and 0.44 at IJ of 4.0-4.1. f RPF
increases to 0.78-1.00 at IJ of 5.2 to 6.1. Based on the trend, we developed damage function on
occurrence of power failures.
2) Number of affected households and houses NPFi for Midori ward and Sakae ward in Yokohama city
show large values over 50,000 households. NPFi for 12 cities and towns in Ibaraki prefecture and 7
cities and towns in Tochigi prefecture show larger values over 20,000 houses. NPFi for 2 cities in
Saitama prefecture and 3 cities and towns in Chiba prefecture also show larger values over 20,000
houses. NPFi for the boundary regions between Tokyo metropolitan areas and Kanagawa prefecture
show the values over 100,000 houses.

1558

3) Damage ratio Rhi for eastern areas in Tochigi prefecture show higher values over 0.9. Rhi for westernareas in Saitama prefecture show higher values over 0.7. Rhi for Midori ward and Sakae ward in
Yokohama city show higher values over 0.7. Damage ratio Rci for 21 cities and towns in Ibaraki
prefecture and 12 cities and towns in Chiba prefecture show values over 0.6.
4) Restoration periods DRP at IJ of 3.0 to 4.5 show 0.3 days to 0.7 days, that is nearly half a day. DRP
for two cities at IJ over 4.5 show 1 day, DRP for a town at IJ of 4.7 shows 2 days and DRP for a city
at IJ of 5.0 shows 5 days. Moreover maximum value of DRP for Kashima city in Ibaraki prefecture
at IJ over 5.0 shows 7 days. DRP for northern areas and coastal areas at Ibaraki prefecture show
over 4 days which is longer than the other areas. On the other hand, DRP for the areas at Saitama
prefecture and Kanagawa prefecture show within 1 day which is relatively shorter. Based on thetrend, we developed damage function on restoration period DRP with seismic intensity IJ

ACKNOWLEDGMENTS
We appreciate valuable cooperation for the related local governments at subject cities, towns, village
and wards and for Chiba branch office, Tochigi branch office, Mito branch office, South Tochigi
branch office and Tsurumi branch office of Tokyo Electric Power Company, Inc. This study wassponsored by the integrated risk management project for complex disasters on large-scale earthquakes
at University of Tsukuba (leader, Professor Y. Yagi).

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Editorial Committee for the Report on the Hanshin-Awaji Earthquake Disaster (1997). “Chapter 5,
Electric Power Facilities.” Report on the Hanshin-Awaji Earthquake Disaster Damage andRestoration of Lifeline Systems, 337-339.
Cabinet Office, Government of Japan (2007). “About 2007 Niigata-ken Chuetsu-oki earthquake Part.9.”
http://www.bousai. go.jp/kinkyu/070724jishin_niigata/070724jishin_niigata.pdf%EF%BC%89.
Hashimoto, S. (2004). “Chapter 7 Electric Power.” Summaries of Report on Damage caused by the2004 Niigata-ken Chuetsu earthquake, 117-122.
Joint Research Committee of Four Societies in Tohoku Regions on the Iwate-Miyagi Earthquake(2009). “Chapter 6, Section 3, Electric Power Facilities.” Report on the 2008 Iwate-Miyagi
Earthquake Disaster, 349-355
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