Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTHE BEHAVIOR OF THE REACTOR BUILDING AT
FUKUSHIMA DAI-ICHI NUCLEAR POWER PLANT
DURING THE GREAT EAST JAPAN EARTHQUAKE
Katsutoshi SUGIOKA1, Rikiro KIKUCHI2 and Katsuichirou HIJIKATA3
1Architectural Engineering Group, Nuclear Seismic Engineering Center,Nuclear Asset Management Department, Tokyo Electric Power Company, Tokyo, Japan
2Manager, Architectural Engineering Group, Nuclear Seismic Engineering Center,
Nuclear Asset Management Department, Tokyo Electric Power Company, Tokyo, Japan
3General Manager, Nuclear Seismic Engineering Center, Nuclear AssetManagement Department, Tokyo Electric Power Company, Tokyo, Japan

ABSTRACT: The GREAT EAST JAPAN EARTHQUAKE which occurred on 11 March2011 struck Fukushima Dai-ichi Nuclear Power Plant and observation records were obtainedat the base mat of reactor buildings. The simulation analysis of the reactor building using
observed records shows that the whole building response is supposed to be basically elastic
during the earthquake. In order to analyze this result, comparison of original design seismic
load and that of simulation analysis based on the observation records was carried out.
Key Words: the Great East Japan Earthquake, Nuclear Power Plant, Reactor Building,Soil-Structure Interaction, Seismic Design

INTRODUCTION
The GREAT EAST JAPAN EARTHQUAKE which occurred on 11 March 2011 struck Fukushima
Dai-ichi Nuclear Power Plant (NPP) and thus observation records were obtained at the base mat ofreactor buildings. The purpose of this report is to show the behavior of the reactor buildings under theearthquake by carrying out the seismic response analysis using the observation records.
Although Fukushima Dai-ichi NPP suffered devastating damage by hydrogen detonation which
results from the loss of cooling capacity because of station black out caused by the tsunamis, thisreport is focused on the effect of the earthquake and the effect of the tsunamis is not intended.
Seismometers are installed in each reactor buildings and seismic observation had been conducted.
And the acceleration time histories on the base mat of reactor buildings were obtained. Maximum
acceleration values from the observation records are shown in Table 1. And maximum response
acceleration values to Design Basis Ground Motion (DBGM) are also shown in Table 1. DBGM is theground motion for seismic safety analysis based on “Regulatory Guide: Reviewing Seismic Design ofNuclear Power Reactor Facilities (2006)”. Maximum acceleration values observed at Unit #2, #3 and#5 during the earthquake were bigger than those of DBGM. Particularly the biggest maximum
acceleration value was observed in the east-west direction of Unit #2.

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Table 1

Observation records at the base mat of Reactor Buildings

Maximum acceleration value
from observation records (Gal)Maximum response acceleration value
to Design Basis Ground Motion (Gal)NSEWUDNSEW

UDUnit #1

460

447

258

487

489

412

Unit #2

348

550

302

441

438

420

Unit #3

322

507

231

449

441

429

Unit #4

281

319

200

447

445

422

Unit #5

311

548

256

452

452

427

Unit #6298

444

244

445

448

415

exceeded DBGM

Estimation of Behavior of Reactor Buildings Using the Observation Records
Method of the Earthquake Response Analysis
The method of simulation analysis in this report is basically elastic response analysis usingobservation records on the base mat of reactor building.
Seismic response of reactor building is calculated by transfer functions from the base mat to eachfloor inputting observation records into the base mat of seismic response analysis model. Figure 1
shows the outline of elastic response analysis in horizontal direction.
Observation records on the base mat are input for the analyses for the reactor buildings. The
response at each floor is calculated as shown in the flowchart.
First, the dynamic soil responses at the embedded part of the building are calculated from one
dimensional wave propagation theory.
Second, the dynamic soil responses are applied to the building as the input motions for thesimulation analysis in horizontal direction. As a result, the responses of the building are evaluatedtaking into account the soil structure interaction. Based on the above, the transfer functions from thebase mat to each floor are calculated.
Third, the earthquake responses of individual parts of the building are obtained by multiplying thetransfer function calculated as above by the Fourier spectrum obtained from the Fourier transform of
the observation records of the base mat.
If the response of the building exceeded elastic range in above analysis, elasto-plastic response
analysis is adopted. As shown in Figure 2, elasto-plastic response analysis is conducted based on theinput motions of the soil that almost reproduce observation records of the base mat.
In the case of Unit #2, the response partially exceeded elastic range and thus the elasto-plastic
response analysis was adopted.

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< Time domain >Acceleration time historyof response on the eachfloor of the building< Frequency domain >inverseFourier transform

Fourier transform ofresponse on each floorof the buildingU (ω)
Fu F(t)Transfer function
(F/B)

0

phase

ampF
π00π

Freq.

Freq.

R H B(ω)

Multiplies transfer function

U (ω)  U (ω)* H (ω)
FB
R B

B

Earthquake
input motion

Shear force

Acceleration time historyof observation record on
the base mat

Observation recordon the basematu (t)Fourier transformU (ω)B

u B(t)B

Fourier transform ofobservation recordon the base mat

phase

amp

SHAKE (One dimensional propagation)
analysisπ000π

Freq.

Fig. 1 Outline of elastic response analysis
Building analysis modelCalculation on one dimensional
propagation theory
Ground Surface

Ground Level

Surface layer

Bottom levelof building

Bottom level of the building

Corrective
horizontalforce

Bearing stratum

Calculation on one dimensional
propagation theory
Depth of the free surface of the basestratum ground (206.0m)●：Observation record on the base mat○：Input motion that reproduce observation
record on the base mat

The free surface ofthe base stratum

Fig. 2 Outline of elasto-plastic response analysis

1534Freq.

Detail of the Earthquake Response Analysis Model
Reactor building is reinforced concrete structure, placed on bedrock and made as rigid as possible.
Figure 3 shows the seismic response analysis model. So-called embedded Sway-Rocking model,
which is composed of the combination of a building model and soil springs, is applied to the analysis.
The building model is a stick model with a concentrated mass located at each floor, taking into accountbending and shear stiffness. Young's modulus of concrete is evaluated from the measured compressive
strength of test pieces sampled from actual building walls.
Damping factor of the building was determined to be 5%. The nonlinear characteristics of shear
walls are determined by the method specified in the guideline for seismic design of nuclear power
plants “JEAC 4601-2008”.
The soil springs for the base mat are employed to consider soil structure interaction. The rotationaland horizontal soil springs underneath the base mat were decided based on the admittance vibration
theory. And those of beside the base mat were based on the Novak’s method. Soil springs were
calculated as complex stiffness depending on frequency as shown in figure 4. Spring constant wasapproximated by maximum value of real part. And damping coefficient was approximated by adopting
the slope of the line through the origin and the point of the imaginary part according to the first natural
frequency of soil-structure interaction model.
The soil properties were taken into account the strain dependency of the stiffness and damping.
Degrading stiffness and damping value according to the strain level were considered and adopted in
the evaluation of soil spring.
Analysis condition is shown in Table 2.

1O.P.55.72

2O.P.47.82

3O.P.39.92

4O.P.32.30

5O.P.26.90

O.P.18.70

6O.P.10.20

7O.P.-2.06

8O.P.-6.06

南北方向断面Fig. 3 Seismic response analysis model

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9Complex stiffness
Real part

Imaginary part

Freq.

Vibration admittance theory
Complex stiffness

Real part

Imaginary part

Freq.

Novak’s method

Fig. 4 Evaluation method of soil springs
Table 2 Analysis condition and physical value
Analysis condition for structure
Stiffness

Young's modulus ofconcrete

Based on material testing
Ec=2.57×104N/mm2 (35.0N/mm2)( ) : compressive strength5%(Based on Strain energy proportional method)

Damping

Analysis conditions for soil-structure interaction
Soilspring

Underneath the base mat

Based on Vibration admittance theory(horizontal and rotational)
Based on Novak's method(horizontal and rotational)

Beside the base mat

Stiffness and damping factors basedon maximum strain levels
Nonlinear

Soil properties
Uplift of the base mat

Seismic Response Analysis Result
The analytical results based on above-mentioned procedures are shown in Figure 5 and Figure 6.
Figure 5 shows the distribution of maximum response acceleration in height for Unit #2 obtained fromthe analysis. Figure 6 shows the maximum shear stress and strain plotted on nonlinear characteristics
of shear wall on each floor.
The maximum shear strain obtained from the analysis is 0.43×103 of the east-west shear wall on 5thfloor. All shear walls only except the above are within elastic range. Therefore, the analysis shows thatthe whole building response is supposed to be basically elastic under the earthquake.

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■
観測値

(cm/s2)

Observation
シミュレーション解析
Simulation

1236

O.P.
(m)
55.72

47.82

98439.92

O.P.
(m)
55.72

観測値
Obs.

Sim.

観測値

観測値
Obs.

シミュレーション解析
Simulation

シミュレー
ション解析

Sim.

2

1523

47.82

2

1534764

39.92

2

985

32.30

651

32.30

0802

26.90

579

26.90

0

737

18.70

472

18.70

0680

10.20

397

10.20

0593

349

-2.06

364-6.06

666

348

-2.06
-6.06

0500

1000

1500

2000

0500

2
Acceleration
加速度(cm/s2) (cm/s )

1000

1500

2000

550

548
541

2
Acceleration
加速度(cm/s2)(cm/s )Fig. 5

Maximum acceleration

88

CRF
5F
B1F

675F
6

Shear stress (N/mm2)

7

Shear stress (N/mm2)(cm/s2)

Observation■シミュレー
ション解析

1F

5434F

5F
1F
CRF
2F
3F
B1F
4F

21003F

2F

B1F

432F

3F

4F

1F
CRF
3F
2F
B1F
4F

2041F

5F

12CRF

50

Shear strain (×10-3)

24

Shear strain (×10-3)

Fig. 6 Maximum shear strain

Comparison of seismic loads condition
Comparison of Seismic Loads
Maximum acceleration value of the observation record on the base mat of Unit #2 under the Great
East Japan Earthquake exceeded that of DBGM. However, the simulation analysis shows the building
response is basically within elastic range.
In order to analyze the reason, original design seismic load was compared to results of simulation
analysis.

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Philosophy of Original Seismic Design
Philosophy of original seismic design is discussed below.
In order to decide the design seismic loads, static and dynamic seismic loads are considered andthe design seismic loads are decided so as to be bigger than above-mentioned two seismic loads. And
the reactor building is designed so as to be within allowable stress.
Amount of rebar arrangement is calculated assuming that only reinforcing bars bear all shear stresscaused by design seismic load. On the other hand, shear wall thickness is decided in such a way thatshear stress to some extent can be covered by only concrete. In addition, shielding performance is also
taken into account in deciding wall thickness. Figure 7 shows the seismic design flow mentioned
above.
In order to decide dynamic seismic load for Unit #2, dynamic responses calculated from the pastobservation records such as ELCENTRO (1940.5.18, NS direction) and TAFT (1952.7.21, EWdirection) are considered. The maximum acceleration values of the records were normalized at 180 gal.
According to the original design documents, Taft and Elcentro were selected by reason of typicalstrong ground motion record. Furthermore, the seismic response analysis model at that time wasdifferent from the present one in soil dissipation damping and so on.
Static seismic load is decided so as to be three times as big as that of the Building Standard Act atthat time. Thus shear coefficient in the first basement was 0.48.
As far as Unit #2 reactor building is concerned, the original design seismic load was mainly
determined by dynamic seismic loads.
As explained above, the original design seismic load depended greatly on engineering judgment.

（START ）Required wall thickness （Required shielding thickness）

Static seismic load
Modifyingequipmentlayout anddesign

Dynamic seismic load

Designseismic
seismicload
load
DesignModifying
Modifyingwall
wallthickness
thickness

Reinforcement
Reinforcementdesign
design（END）

Fig. 7 Seismic design flow

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Comparison Result of Seismic Loads
Figure 8 compares shear stress between seismic loads such as design seismic load, static seismic load,
dynamic seismic load and simulation analysis results. According to figure 8, the shear stress acting tounit #2 reactor building under this earthquake is almost equivalent to that of design seismic load.
Simulation
O.P.
(m)
55.72

Dynamic

Static
O.P.
(m)
55.72

Design

47.82

47.82

39.92

39.92

32.30

32.30

26.90

26.90

18.70

18.70

10.20

10.20

-2.06

Simulation

StaticDynamic

Design

-2.06
0.00

1.00

2.00

3.00

0.00

21.00

2.00

3.00
2

Shear Stress（N/mm ）Shear Stress（N/mm ）NS direction

EW direction

Fig. 8 Comparison of original design sheer stress and that of simulation analysis

Conservatism of Original Dynamic Response Analysis Model
Ground motions for original dynamic response analysis were Taft and Elcentro whose maximum
accelerations were normalized at 180 gal. However, the shear stress caused by the motions was almost
equal to that of response analysis results using observation records during the Great East Japan
Earthquake, which were 550 gal at a maximum on the base mat in reactor building Unit #2.
In order to analyze the reason, soil spring evaluation which were clearly different between original
dynamic response analysis and this simulation analysis is focused and examined.
Table 3 shows the result of comparison. The value of soil spring stiffness and damping in theeast-west direction are shown in Table 3.
Horizontal stiffness value besides the base mat in original design was almost ten times bigger thanthat of simulation analysis. And rotational stiffness was not considered in original design.
Damping value in original design was 5% at any frequency, although that can be evaluated bigger
by far if soil dissipation damping due to soil-structure interaction were considered. This is thought tobe that evaluation method of soil dissipation damping had not been established in those days. On theother hand, in the simulation analysis, approximate damping coefficient which depends on frequency
is considered in order to evaluate soil dissipation damping properly. Thus, the damping coefficientbesides base mat was calculated based on Novak’s method and that of underneath the base mat wasbased on vibration admittance theory.

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The difference in evaluation of soil springs as above was supposed to be one of the reasons why
original dynamic analysis model was conservative so as to give bigger shear stress in analysis results.
Because design seismic load was originally evaluated using conservative model, the shear stress
distribution by original response analysis model was thought to be as same level as that of simulation
analysis although maximum acceleration of ground motions for original dynamic response analysis
was much smaller than that of observation records on the base mat during the Great East Japan
Earthquake.

Table 3 Comparison of soil springs evaluation
Original Design

Analysis model(Elastic response analysis)
Stiffness

Horizontal: 5.34×107kN/m
Rotational: Not considered

Soil Spring
BesidesBase mat

Simulation
O.P.
(m)
55.72

147.82239.92332.30426.90518.70610.207-2.068-6.06

9(Elasto-Plastic response analysis)
Horizontal : 2.40×106kN/m
Rotational : 1.47×106kN/m

Damping5%（at any frequency）[Damping coefficient]
Horizontal:4.81×105kNs/m
Rotational:8.97×107kNm/rad

Stiffness

Horizontal: 4.36×107kN/m
Rotational: 3.90×1010kNm/rad

Horizontal : 5.41×107kN/m
Rotational : 5.24×1010kNm/rad

Damping5%（at any frequency）[Damping coefficient]
Horizontal: 2.00×106kNs/m
Rotational: 5.74×108kNm/rad

Soil Spring
UnderneathBase mat1540

CONCLUSIONS
The maximum acceleration observed at Fukushima Dai-ichi NPP during the Great Japan Earthquake
exceeded the maximum response acceleration of DBGM. However, the result of simulation analysis
using the observation records shows that the whole building response was basically elastic under theearthquake.
In order to analyze the reason why the response was almost elastic range, the original seismic loadwas compared to the result of simulation analysis. In determining the design seismic load, both staticand dynamic seismic loads are taken into account. The original dynamic load for Unit #2 Reactor
Building was based on the response analysis using the past observation records at other sites such asTaft. The static seismic load is three times as big as that of the Building Standard Act at that time. Asfor Unit #2 reactor building, design seismic load was mainly determined by dynamic seismic load. The
comparison of original design with simulation result shows that shear stress supposed in original
design and that of simulation analysis were almost same level. This is thought to be that the soil
dissipation damping was scarcely considered in original design model which was Sway-Rocking
model generally employed in those days.
Thus, although the maximum acceleration value of the ground motion for original design was
smaller than that of the Great East Japan Earthquake, the analysis model was so conservative that theshear stress considered in original design was almost as same level as that in the simulation analysis
for this earthquake. This is why the whole building response is basically elastic under the earthquake.

REFERENCES
Tokyo Electric Power Company (2011). “The Report on the Analysis of Observed Seismic Data
collected at Fukushima Daiichi Nuclear Power Station and Fukushima Daini Nuclear Power Station
pertaining to the Tohoku-Taiheiyou-Oki Earthquake.” (in Japanese)
Tokyo Electric Power Company (2011). “Fukushima Daiichi Nuclear Power Station Unit No.1 Reporton Earthquake Response Analysis of the Reactor Building, Important Equipment and Piping System
for Seismic Safety using Recorded Seismic Data of the Tohoku-Chihou-Taiheiyo-Oki Earthquake inthe Year 2011” (in Japanese)
Japan Electric Association (2009). “JEAC4601-2008 Technical Code for Seismic Design of Nuclear
Power Plants”(in Japanese)
Architectural Institute of Japan (2010). “AIJ Standard for Structural Calculation of Reinforced
Concrete Structures” (in Japanese)

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