NIOM ANALYSIS OF THE ACCELERATION RECORDS OBSERVED ATVERTICAL ARRAY IN THE KASHIWAZAKI-KARIWA NUCLEAR POWER PLANT

Hidenori MOGI1), Santa Man, SHRESTHA1), Hideji KAWAKAMI2), and Shinya OKAMURA3)

1)Foundations and Earthquake Engineering Lab., Graduate School of Science and Engineering, Saitama Univ.2)Foundations and Earthquake Engineering Lab., Geosphere Research Institute, Saitama Univ.

3)Foundations and Earthquake Engineering Lab., Dept.of Civil and Environmental Engineering, Saitama Univ.

ABSTRACT

The Kashiwazaki-Kariwa Nuclear Power Plant suffered extreme shaking during the 2007 Niigata-ken Chuetsu-oki earthquake. Accelerograms observed at the dense seismometer array in the plantare now open to the public and will provide valuable knowledge. The temporal changes of S-wavevelocity were examined based on the vertical array records observed during the mainshock and theevents before and after it. It was found that the S-wave velocity in the layers (ground–50m depthand 50–100 m depth) decreased significantly during the principal motion of the mainshock, indicatingnonlinear behavior. Whereas nearly linear behavior was observed in the bedrock layer (below 100 mdepth). It was also found that the S-wave velocity increased in the layers above 100 m depth soon afterthis motion, indicating no major liquefaction in these layers.

KEYWORDS: NIOM analysis, vertical accelerometer array, nonlinear behavior

1. INTRODUCTION

The 2007 Niigata-ken Chuetsu-oki earthquakecaused severe damage in Niigata Prefecture. Dam-age was also observed in the Tokyo Electric PowerCompany (TEPCO)’s Kashiwazaki-Kariwa nuclearplant located in the vicinity of the hypocenter.The seismic observation (accelerograms) had beenrecorded in a dense seismometer array located atthe plant site. TEPCO has published records ofdifferent seismic events: before, during, and afterthe Niigata-ken Chuetsu-oki earthquake, observedat the dense seismometer array (TEPCO 2008).These records provide useful information for vari-ous examinations such as seismic response of thestructure, seismic response of the ground, and thesoil-structure interaction.

Various laboratory tests have been conductedby many researchers (e.g. Seed and Idriss 1970,Hardin and Drnevich 1972a, Hardin and Drnevich1972b, Katayama et al. 1986, Hatanaka et al. 1988,Sun et al. 1988) to examine nonlinear properties ofdifferent soil types and revealed that soil propertiesare affected by various factors such as shear-strainlevel, confining stress, void ratio, the extent ofdisturbance to the specimen and so on.

In-situ examination of the nonlinear propertyof soil utilizes vertical array records of actualearthquakes because a strain level large enough tocause nonlinear behavior in in-situ soil is unattain-able by artificial excitations. So the method usedis inversion calculation using multiple reflection

analysis of SH waves and equivalent linear anal-ysis based on the constitutive relationship of soils(Ohta 1975, Tokimatsu et al. 2008, Tokimatsu andArai 2008) Tokimatsu et al. conducted inversionanalysis of the vertical array records observed inthe Kashiwazaki-Kariwa NPP and pointed out asignificant reduction of the shear moduli in theHolocene and Pleistocene sand layers during themainshock of the 2007 Niigata-ken Chuetsu-okiearthquake (Tokimatsu et al. 2008, Tokimatsu andArai 2008). However, the estimated shear moduliin the study are time-independent throughout eacharray record as in usual equivalent linear analyses, sothe temporal changes of the moduli during a singleearthquake have not been examined.

Kawakami et al. developed the Simplified InputOutput Relation Method (SIORM) (Kawakami andBidon 1997) and Normalized Input-Output Mini-mization (NIOM) method (Kawakami and Haddadi1998, Haddadi and Kawakami 1998a) to examinewave propagation velocity from the vertical arrayrecords. The validity of these methods has beenshown with different vertical array records. In addi-tion, the results from the NIOM analysis of the 1995Hyogo-ken Nambu earthquake at the Port Islandvertical array site clearly showed the liquefaction ofthe surface layer by detecting a decrease in S-wavevelocity in the top layer by analysis of differentparts of the aftershocks (Hadaddi and Kawakami,1998b). These results showed the temporal changesin the characteristics of soil at different layers and are

– 21 –

useful for engineering purposes. On the other hand,nonlinear behavior of the relatively rigid groundwhere important facilities such as nuclear powerplants are located has not been closely examined sofar.

In this study, using the NIOM method, recordsof the mainshock and the aftershocks of the 2007Niigata-ken Chuetsu-oki earthquake at the verticalarray of the PR Hall (KSH) at the Kashiwazaki-Kariwa nuclear power plant were analyzed. Also,using the previous earthquake records at the samearray site, the temporal variation of S-wave velocitywas examined. It was observed that the S-wavevelocity decreased significantly in the surface layer(surface to 50 m depth) and intermediate layer(50–100 m depth) during the principal motions of themainshock. However, the S-wave velocity startedto increase soon after this motion, indicating nooccurrence of liquefaction in these layers. Onthe other hand, in the bedrock layer (below 100 mdepth), the S-wave velocity variation was negligible,showing nearly linear behavior even during theprincipal motions of the mainshock.

2. OUTLINE OF NIOM METHODThis section describes the outline of NIOM

method developed by Kawakami and Haddadi(1998).

The input-output system can be related bymeans of a transfer function H(ω). In a frequencydomain, the output G(ω) is given by

G(ω) = H(ω)F (ω), (1)

where F (ω) and G(ω) are the Fourier transforms ofthe input f(t) and the output g(t).

Since the transfer function solely dependsupon the physical characteristics of the system, weassume that the same transfer function satisfies therelationship between input and output models. Sowe can write

Y (ω) = H(ω)X(ω), (2)

where X(ω) and Y (ω) are the Fourier transformsof the input and output models x(t) and y(t),respectively.

The inverse Fourier transform of input modelX(ω) can be written as

x(mΔt) =1

NΔt

N−1∑i=0

X(ωi) exp(

j2πim

N

). (3)

At t = 0, i.e., m = 0, the amplitude of the inputmodel, x(0), is normalized to unity, then Eq. (3)becomes

1NΔt

N−1∑i=0

X(ωi) = 1. (4)

To get the simplified input and output models,the mean value of the squared Fourier amplitude

and its time derivatives are minimized subject tothe above constraint. Thus, the Lagrange multipliermethod gives

L =N−1∑i=0

[cX |X(ωi)|2 + kXω2

i |X(ωi)|2

+ cY |Y (ωi)|2 + kY ω2i |Y (ωi)|2

]

− λ

{1

NΔt

N−1∑i=0

X(ωi) − 1

}, (5)

where λ is the Lagrange multiplier, cX and cY arethe weighing constants for corresponding squaredFourier amplitude, and kX and kY are the weighingconstants for its time derivatives. The samerelationship of weighing constants for input andoutput is considered as

kX

cX=

kY

cY. (6)

The contribution of high frequency components canbe decreased by increasing the value of kX .

Substituting Eqs. (2) and (6) in Eq. (5) andminimizing the equation thus obtained as

∂L

∂λ=

∂L

∂X(ωi)=

∂L

∂X∗(ωi)= 0, (i = 0, . . . , N−1),

(7)where ∗ denotes the complex conjugate.

After minimization, the input model X(ωi) andoutput model Y (ωi) are obtained as follows.

X(ωi) = NΔt

1�1 +

kX

cXω2

i

�(cX + cY |H(ωi)|2)

N−1�n=0

1�1 +

kX

cXω2

n

�(cX + cY |H(ωn)|2)

,

Y (ωi) = H(ωi)X(ωi). (8)

Lastly, the inverse Fourier transforms of theinput model X(ω) and output model Y (ω) willgive the simplified input model x(t) and y(t) intime domains. As mentioned above, the NIOMmethod is a simple input-output analysis techniquein which the transfer function is calculated from twoobservation data satisfying input x(t) at x(0) = 1.It is similar to a receiver function ([?]). In a receiverfunction, input x(t) should be assumed as a suitablepulse, however, in the NIOM method, the adjustmentfeatures are included to get simplified input andoutput waveforms.

3. KSH VERTICAL ARRAY AND PARAME-TERS FOR NIOM ANALYSISTo investigate the temporal change of S-wave

velocity before, during, and after the main shock, theobservation records at the PR Hall (KSH) vertical

– 22 –

42.6

m5.

832

.216

.470

.435

.045

.0

S waveP wave

Elastic wave speed (m/s) (Depth) (Elevation)Geology /Seismometer

(Depth)(Elevation) (Thickness)

Recent sand deposit

Banjin formation

Yasuda formation

Nishiyama formation

Seismometer location

(PS logging data at the time of seismometer installation)

Fig. 1 Soil profile at the KSH site provided by TEPCO (2008) with slight modification.

array (TEPCO 2008) were used in this study. Asshown in Figure 1, this vertical array consists of fourobservation points from SG1 (ground surface) toSG4 (250 m depth). Each observation point recordsEW, NS, and UD components of the acceleration. Inthis study the NS and EW components were used.Though the NS direction is tilted 18◦54′51′′ towardsthe east, we simply used the terms NS and EW.

If f(t) and g(t) are the two observation recordsrecorded at surface and underground observationpoints, the output model y(t) obtained by theNIOM analysis can be interpreted as the record ofobservation at an underground observation point asif a pulse x(t) is given as input in the observationpoint above. Therefore if input model x(t) at timet = 0 is a pulse with maximum amplitude of oneand vertical incidence is assumed, a peak appearingon the output model y(t) at negative time represents

the incident wave (raising wave) whereas a peakappearing at positive time represents a reflectedwave (falling wave) at the underground observationpoint. Then from the four observation points ofthe vertical array, the three combinations SG1–SG2,SG2–SG3, and SG3–SG4 were considered andNIOM analysis was carried out for these threecombinations to find the S-wave propagation time.The time given by the incident (wave) peaks showsthe wave propagation time. Except for SG1–SG2,when the above observation point is not the surfaceof earth, the arrival time of descendent waves willbe influenced by the travel time of reflected wavesfrom the surface. In such cases, the propagationtime intervals for reflected waves are different. Soin this study, peaks appearing at negative time,i.e., the propagation time of incident waves, weremainly examined. The parameters used for NIOM

– 23 –

analysis were cX = cY = 1 and kX = 0.001.The sampling rate of the observed data was 0.01 s.The data obtained from the input model X(ω) andoutput model Y (ω) as given in Eq. (8) of theNIOM analysis were increased by a factor of 16 byadding trailing zeros. Then, the time interval of theinput and output model obtained by inverse FourierTransform was interpolated by 1/16.

4. ESTIMATION METHOD OF S-WAVE VE-LOCITYThe elastic wave speed shown in Figure 1

was obtained by PS logging. From PS logging,the S-wave velocities of five layers from surfaceto 250 m depth were 310, 350, 500, 580, and 640m/s. Among these layers, we considered the S-wavevelocity in the 310 m/s layer (recent sand duneand the upper part of the Banjin formation) as β1,the 350 m/s layer (the lower part of the Banjinand Yasuda formations) as β2, and the 500 m/slayer (the Nishiyama formation) as β3. We calledthese layers the surface layer, intermediate layer, andbase layer, respectively. It was assumed that theS-wave velocity in each layer changes depending ontime and earthquake event considered. At first, theS-wave velocity of each layer of the Nishiyama layerwas assumed to have the same value as that of thecorresponding velocity obtained by PS logging butvarying by a factor of α. β3 was estimated basedon the propagation time t4−3 between SG4–SG3obtained by NIOM analysis.

β3 = 500 α (m/s),α = T4−3/t4−3. (9)

Here, T4−3 is the S-wave propagation time (0.271 s)in the SG4–SG3 layer obtained by PS logging.Getting β3 from Eq. (9), β2 and β1 were estimatedby the following equations using the propagationtimes t3−2 and t2−1 obtained from the NIOManalysis.

β2 =32.2

t3−2 − 16.4/β3(m/s),

β1 =42.6

t2−1 − 5.8/β2(m/s). (10)

Now, if we let the propagation time be t, propagationvelocity be β, and propagation distance be L, thenfrom the relationship β = L/t, the relation betweenpropagation velocity error Δβ and propagation timereading error Δt can be shown as

Δβ =β2

LΔt. (11)

Here, if propagation time reading error is substitutedby sampling rate Δt = 0.01 s, the propagationvelocity error Δβ can be estimated as 15 m/s for allthree layers.

5. ANALYSIS RESULTS5.1 Analyzed Accelerograms

The earthquake accelerograms analyzed in thispaper are summarized in Table 1. Among these,earthquakes a to x are aftershocks of the 2007Niigata-ken Chuetsu-oki earthquake. Similarly, A toC are earthquakes that occurred before the Niigata-ken Chuetsu-oki earthquake and were included inorder to consider the probable changes in the groundstiffness from the time of PS logging and the timebefore the Niigata-ken Chuetsu-oki earthquake. Theepicenter location and the relationship between theepicentral distance and focal depth are shown inFigures 2a and 2b, respectively. All the earthquakeswere located near the vertical array as shown inFigure 2, so we can assume vertical incidence ofsesimic waves during the principal motions in theaccelerograms.

Figure 3 shows accelerograms recorded at thevertical array during the Niigata-ken Chuetsu-okiearthquake. The record at SG1 (at ground surface)has a simpler shape than those underground due toloss of high frequency components.

5.2 Results of NIOM AnalysisIn NIOM analysis for the earthquakes that

occurred before and after the Niigata-ken Chuetsu-oki earthquake, 2.5-s time intervals of the principalmotion of the S-wave part were analyzed. In theanalysis of the mainshock, a moving window of 4.0-sduration was used from 26 to 150 s in 2 s increments.A cosine taper time window of 0.25 s intervals onboth sides was used to select the analysis interval.

Figure 4 shows the results of NIOM analyses,(a)–(c) for earthquake C (before the Niigata-kenChuetsu-oki earthquake), (d)–(f) for the principalmotion of the Niigata-ken Chuetsu-oki earthquake,(g)–(l) for the coda of the Niigata-ken Chuetsu-okiearthquake, and (m)-(o) for earthquake x (aftershockon 25 March 2008). The diagrams are aligned fromleft to right in the order of SG1–SG2 to SG3–SG4.In these diagrams, the thick solid and the thick dottedlines respectively show the output models of theEW and NS components whereas the thin dottedlines show the input models of the EW component.The input model was the simplified pulse from theupper seismometer reading and the output modelwas the simplified wave obtained from the lowerseismometer reading. For example, for the (a)SG1–SG2 layer, the input model was of SG1 andthe output model was of SG2. In this diagram, wavearrivals at SG1 and SG2 can clearly be seen at 0 s and-0.184 s, respectively. So the wave propagation timefor the interval between SG1 and SG2 was 0.184 s.

The output models for SG3–SG4 (Fig. 4c, f,l, and o) show clear peaks at about -0.28 s, andthe variation of peak time for different earthquakesis small. This indicates that the S-wave velocitybetween SG4 and SG3 was almost unchanged even

– 24 –

Table 1 Source parameters of the earthquakes analyzed in this study.

Date Time Epicenter MJMA Epicentral Depth(yyyy/mm/dd) ◦E ◦N Distance (km) (km)

A 2005/11/04 03:05 138.467 37.432 2.7 12 27B 2005/11/13 16:51 138.477 37.440 3.2 11 28C 2006/03/12 23:12 138.477 37.444 2.4 11 28Mainshock 2007/07/16 10:13 138.608 37.557 6.8 16 17a 2007/07/16 10:17 138.510 37.402 4.0 8 20b 2007/07/16 10:18 138.547 37.505 4.9 11 18c 2007/07/16 10:22 138.567 37.535 3.9 13 17d 2007/07/16 10:24 138.522 37.482 3.7 10 19e 2007/07/16 10:25 138.433 37.542 3.0 20 22f 2007/07/16 10:28 138.528 37.422 3.9 6 19g 2007/07/16 10:53 138.582 37.523 3.1 12 21h 2007/07/16 11:00 138.565 37.457 3.7 5 22i 2007/07/16 15:00 138.577 37.442 2.0 3 19j 2007/07/17 05:28 138.567 37.455 2.5 5 20k 2007/07/18 00:46 138.572 37.483 2.1 8 19l 2007/07/19 05:27 138.528 37.542 2.3 15 18m 2007/07/20 21:54 138.568 37.447 3.6 4 20n 2007/07/21 18:51 138.550 37.430 1.7 5 19o 2007/07/25 00:35 138.553 37.420 2.4 4 17p 2007/07/25 06:52 138.720 37.532 4.8 17 24q 2007/07/30 23:15 138.547 37.418 1.8 5 18r 2007/08/03 18:45 138.548 37.440 2.4 5 18s 2007/08/10 02:04 138.547 37.395 3.2 5 18t 2007/09/18 01:35 138.570 37.445 3.4 4 19u 2007/10/04 13:02 138.573 37.452 1.9 5 18v 2007/11/30 18:33 138.575 37.450 1.9 4 20w 2008/02/04 12:02 138.608 37.467 2.3 6 17x 2008/03/25 10:54 138.563 37.450 2.6 5 20

during the strong motions. Meanwhile, in theresults for the surface layer (SG1–SG2) and theintermediate layer (SG2–SG3), a change in thetime of peak appearance in the output models forthe mainshock and the aftershock can clearly beseen. This indicates changes of S-wave velocity.The output model shows a clear peak even in theprincipal motion of the Niigata-ken Chuetsu-okiearthquake. It should be noted that no suchclear peak could be found in the result for therecords of the 1995 Hyogo-ken Nanbu earthquakeobserved at Port Island where major liquefactionoccured (Hadaddi and Kawakami, 1998b). Althoughsettlements of about 15 cm were reported in the KSHsite (Tokimatsu and Arai, 2008a and 2008b), it canbe concluded that there was no major liquefaction atthe site.

5.3 Temporal Change of S-wave Velocity dur-ing, before, and after the 2007 Niigata-kenChuetsu-oki EarthquakeFigure 5 shows the S-wave velocities estimated

by Eqs. (9) and (10). S-wave velocities for thebase, intermediate, and surface layers are shown bysquares, triangles, and circles, respectively. To showthe seismic intensity at each time window, the RMSvalues of velocity amplitudes during the same time

window are shown by the same symbols in the lowerdiagrams.

Figure 5a shows the S-wave velocities duringthe earthquakes A to C that occurred before theNiigata-ken Chuetsu-oki earthquake. The averagevalue of these velocities for the base layer β3

was 483 m/s, which is almost the same as thevalue estimated by PS logging (500 m/s). On theother hand, the average of the S-wave velocitiesfor the surface layer β1 was 255 m/s and for theintermediate layer β2 was 305 m/s, which are 10to 20% smaller than those measured by PS logging(β1 = 310 m/s, β2 = 350 m/s). These averagedvalues of S-wave velocity are shown by horizontaldotted lines in the diagrams and used as initial valuesfor the comparison of the results of the mainshockand aftershocks.

Figure 5b shows the S-wave velocities dur-ing the mainshock of the Niigata-ken Chuetsu-okiearthquake. The horizontal axis is the center ofthe time window considered. In the results for thebase layer, the velocity decreased slightly during theprincipal motions from 30 to 40 s, and the estimatedvelocity then increased to the initial value soonafterwards. This indicates that the base layer wasnot affected much even by the strong motions duringthe mainshock. On the contrary, large reductions

– 25 –

138.5

37.5

A B

C

a

b

c

d

e

f

g

h

i

jk

l

mn

o

p

q

r

s

t

uv

wx

Mainshock (M6.8)

0 10 km

Kariwa

Kashiwazaki

Ojiya

Izumosaki

Nagaoka

Tokamachi

Tsubame

Niigata

Yahiko

Joetsu

Sea of Japan

37.2

37.8

138.9 E

N

10 20

10

20

30

A

B

C

a

b c

d

e

f

gh

ij

k lm

n

o

p

qrs

tu

v

w

x

Epicentral Distance (km)

Foc

al D

epth

(km

)

Mainshock

(a)

(b)

Kashiwazaki -Kariwa NPP

0

Fig. 2 (a) Epicenter map and (b) relationship between epicentral distance and focal depth of the analyzed events.

0 100-250

-200

-150

-100

-50

0

50

100 500

0 100-250

-200

-150

-100

-50

0

50

100 500

Time (s)Time (s)

Ele

vatio

n (m

)

(cm/s/s) (cm/s/s)

EW NS

SG1

SG2

SG3

SG4

SG1

SG2

SG3

SG4

Fig. 3 Accelerograms of the 2007 Niigata-ken Chuetsu-oki earthquake at the KSH site.

of S-wave velocity can be seen in the results forthe surface and the intermediate layers. At 40 s,

the values were 125 m/s for the EW and 116 m/sfor the NS component in the surface layer and 223

– 26 –

-1 0 1-0.5

0.0

0.5

1.00.

366

-1 0 1-0.5

0.0

0.5

1.0

0.16

9

-1 0 1-0.5

0.0

0.5

1.0

0.28

7

-1 0 1-0.5

0.0

0.5

1.0

0.21

1

-1 0 1-0.5

0.0

0.5

1.0

0.15

1

-1 0 1-0.5

0.0

0.5

1.0

0.28

3

-1 0 1-0.5

0.0

0.5

1.0

0.18

3

-1 0 1-0.5

0.0

0.5

1.0

0.15

2

-1 0 1-0.5

0.0

0.5

1.0

0.27

8

Mai

nsho

ck 3

6-40

sM

ains

hock

58-

62 s

Mai

nsho

ck 1

18-1

22 s

(i)

(k) (l)

(h)

(d) (e) (f)

(g)

0

0.18

4

SG1-SG2

EW

NS

-1 0 1-0.5

0.0

0.5

1.0

-0.5

0

0.5

1.0

0.13

8

SG2-SG3

-1 0 1-0.5

0

0.5

1.0

0.28

2

SG3-SG4

-1 0 1

2006

/03/

12 2

3:12

M2.

4 (b)(a) (c)

(j)

-1 0 1-0.5

0.0

0.5

1.0

-0.2

22

EW

NS

-1 0 1-0.5

0.0

0.5

1.0

-0.1

46

-1 0 1-0.5

0.0

0.5

1.0

-0.2

83

2008

/03/

25 1

0:54

M2.

6 (n)(m) (o)

Time (s) Time (s) Time (s)

Fig. 4: Results of NIOM analyses (a)–(c) for the earthquake at 2006/03/12 23:12 M2.4 (before the Niigata-kenChuetsu-oki earthquake), (d)–(f) for the Niigata-ken Chuetsu-oki earthquake 36–40 s, (g)–(i) 58–62 s, (j)–(l)118–122 s, and (m)–(o) aftershock at 2008/03/25 10:54 M2.6. The results for SG1–SG2, SG2–SG3, and SG3–SG4are shown in the diagrams from left to right at each row, respectively. In those diagrams, the thick solid line andthe thick dotted line indicate the output model for the EW and NS components, respectively, and the thin dottedline indicates the input model of the EW component.

m/s for the EW and 245 m/s for the NS componentin the intermediate layer, which indicated nonlinearbehavior of the soil due to the large amplitudes of theseismic waves during the mainshock. Soon after theprincipal motions, the velocities increased graduallywith a decrease of seismic intensity during the coda

as shown in Figure 5e.In the results for the aftershocks shown in

Figure 5c, we can observe the gradual increase ofthe S-wave velocities in the surface and intermediatelayers but the velocities were still smaller thanthe average values even after eight months. This

– 27 –

0

100

200

300

400

500

600

(b) Mainshock of the Chuetsu-oki Earthquake

Days after the Chuetsu-oki Earthquake (2007/07/16 10:13)0.01 0.1 1 10 100

07/0

7/16

10:

1707

/07/

16 1

0:18

07/0

7/16

10:

2207

/07/

16 1

0:24

07/0

7/16

10:

28

07/0

7/16

10:

5307

/07/

16 1

1:00

07/0

7/16

15:

00

07/0

7/17

05:

28

07/0

7/18

00:

46

07/0

7/19

05:

2707

/07/

20 2

1:54

07/0

7/21

18:

5107

/07/

25 0

0:35

07/0

7/25

06:

5207

/07/

30 2

3:15

07/0

8/03

18:

4507

/08/

10 0

2:04

07/0

9/18

01:

3507

/10/

04 1

3:02

07/1

1/30

18:

3308

/02/

04 1

2:02

08/0

3/25

10:

54

EWNS

(c) Aftershocks

05/1

1/04

03:

0505

/11/

13 1

6:51

06/0

3/12

23:

12

(a) Before the Chuetsu-oki Earthquake

0

100

200

300

400

500

600

Time (s)30 40 50 60 70 80 90 100 110 120 130 140 150

254 (m/s)306 (m/s)

484 (m/s)

S w

ave

velo

city

(m

/s)

Fig. 5: Temporal change of the S-wave velocities at each layer estimated from the records of (a) earthquakesbefore the Niigata-ken Chuetsu-oki earthquake, (b) the Niigata-ken Chuetsu-oki earthquake, and (c) aftershocks.The broken lines indicate the average velocities shown in diagram (a).

indicates that once the soil layer was nonlinearizedby strong ground shaking, the effect remained formore than several months.

5.4 Relationship between Shear Modulus andShear StrainThe relationship between shear modulus and

shear strain was examined based on the S-wavevelocities obtained from NIOM analysis. Thenormalized shear mudulus is defined as

G/G0 = β2/β20 (12)

where G is the shear modulus, β is the S-wavevelocity, and the suffix 0 indicates linear property.Assuming that the soil property remained linearduring the earthquakes that occurred before theNiigata-ken Chuetsu-oki earthquake, the averageS-wave velocity estimated from the earthquakesbefore the Niigata-ken Chuetsu-oki earthquake wasused as β0.

Because shear strain was not observed in thesite, we defined average strain ε as

ε = VRMS/β (13)

where VRMS is the RMS value of the velocitywaveform (Figs 5d–f) during the corresponding timewindow. Eq. (13) is based on the one-dimensionalpropagation of seismic waves as given by

ε =∂u(z, t)

∂z=

∂u(z, t)β ∂t

, (14)

where u is the displacement of seismic waves andz is the coordinate axis along the wave propagationdirection.

Figures 6a–c show the normalized shear mod-ulus reduction for the three layers. As we pointedout earlier, no significant nonlinear behavior wasobserved in the result for the base layer (Fig. 6c).However, the shear strain reached about 0.08%during the principal motion.

In the intermediate layer, the shear modulusdecreased to G/G0 = 0.6 at the strain level ofε =0.1–0.2% (Fig. 6b). Soon after, the shearmodulus gradually increased to about 0.9, andthis process formed a relationship between shearmodulus and shear strain. For the surface layer, it isdifficult to make a quantitative discussion because ofthe large variation and the anisotropical propagationvelocity in the results. However, we can confirm thatthe maximum value of the strain was between 0.1and 1%, and the shear modulus decreased to aboutG/G0 = 0.2.

Because the surface and intermediate layers aresand dune deposits, we compared laboratory testresults of a sand specimen for reference. Figure 6dshows the shear modulus reduction of Fujisawa sandobtained by Katayama et al. (1986) (also included in[?]). The undisturbed specimen was sampled from5 to 9 m depth by the freeze-and-block technique.In-situ S-wave velocity was 260 m/s. This value isclose to that of the surface layer at the KSH site.

The solid and dotted lines show the shearmodulus reduction obtained from the undisturbedand disturbed specimens, respectively. The disturbedspecimen had been remolded to have a void ratio,e, similar to the undisturbed one. In the figure, theshear moduli of the undisturbed and the disturbedspecimens were normalized by the initial shear

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0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

40

50

60

70

8090

100

110

120

130

140

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

30

40

50

607080100

120

140

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4050

6070

120

Strain (%)

-210 -110-310 1-410-510-610 -210 -110-310 1-410-510-610

-210 -110-310 1-410-510-610

Strain (%) Strain (%)

EW NS

Before Chuetsu-oki Eq.Chuetsu-oki Eq.Aftershock

Strain (%)

-210 -110-310 1-410-510-6100

0.2

0.4

0.6

0.8

1.0

1.2

1.4

(a) Surface Layer (b) Intermediate Layer

(c) Base Layer (d) Fujisawa Sand

Fig. 6: (a)–(c) Normalized shear modulus reduction relationship for the three layers at the KSH site based on theS-wave velocity shown in Fig. 5. Numbers at the results of the mainshock indicate center time of the time-window.(d) Laboratory test results of Fujisawa sand obtained by Katayama et al. (1986) shown here for reference. In thisdiagram, the results for both disturbed and undisturbed samples were normalized by the modulus for undisturbedsamples at 1.0×10-3% strain.

modulus of the undisturbed specimen at 1.0×10-3%strain. The shear modulus of the disturbed specimenat 1.0×10-3% strain was about half of that for theundisturbed one whereas those at large strains werealmost identical.

Comparing the results of the surface layerand the undisturbed soil columns obtained fromthe laboratory test (Fig. 6a and d) shows thatthe reduction relationship obtained by the NIOManalysis of the mainshock records is similar to thelaboratory test results. Also, the degradation ofthe shear modulus observed in the surface and theintermediate layers after the mainshock must beassociated with disturbance caused by the large shearstrain during the mainshock.

6. CONCLUSIONSWe examined the temporal changes of S-wave

velocity based on the vertical array records in theKashiwazaki-Kariwa nuclear power plant observedduring, before, and after the 2007 Niigata-kenChuetsu-oki earthquake. The major conclusions ofthis study are

1) The S-wave velocity before the Niigata-kenChuetsu-oki earthquake for the base layer wasalmost the same as estimated by PS logging.However, the S-wave velocities for the surfaceand intermediate layers were 10 to 20% smallerthan those measured by PS logging.

2) In the base layer, a very small reduction of veloc-ity was observed during the principal motions,and the estimated velocity then increased to the

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initial value soon afterwards. This indicates thatthe base layer was not affected much even bystrong motions during the mainshock.

3) Large reductions of S-wave velocity were seen inthe surface and intermediate layers indicatingnonlinear behavior of the soil due to the largeamplitude of the seismic waves during themainshock. Soon after the principal motions,the velocities increased gradually with a de-crease of seismic intensity during the coda.

4) During the aftershocks, there was a gradualincrease in the S-wave velocities in the surfaceand intermediate layers but they are still smallerthan the average values even after eight months.This indicates that once the soil layer wasnonlinearized by strong ground shaking, theeffect remained after more than eight months.

5) The normalized shear modulus reduction rela-tionship obtained by the NIOM analysis ofthe mainshock records was similar to thelaboratory test results. The degradation ofthe shear modulus observed in the surface andthe intermediate layers after the mainshock isassociated with disturbance caused by the shearstrain during the mainshock.

ACKNOWLEDGMENTThe authors would like to thank the Tokyo

Electric Power Company (TEPCO) for providing theaccelerograms used in this study.

REFERENCESHaddadi, H. R. and H. Kawakami, (1998a)

“Modeling Wave Propagation by using NormalizedInput-Output Minimization (NIOM) Methodfor Multiple Linear Systems”, StructuralEng./Earthquake Eng., V.15, (No. 1), pp.29s–39s.

Hadaddi, H. R. and H. Kawakami, (1998b)“Effect of Liquefaction on Ground Motion duringthe Hyogoken-nanbu Earthquake, 1995, in Japan byUsing the NIOM Method”, The Effect of SurfaceGeology on Seismic Motion, Irikura, Kudo, Okadaand Sasatani (editors), Balkema, Rotterdam, V.2,pp.1015–1022.

Hardin, B. O. and V. P. Drnevich, (1972a)“Shear Modulus and Damping in Soils: Mea-surement and Parameter Effects”, J. Soil Mech.Foundations Div. , V.98, pp.603–624.

Hardin, B. O. and V. P. Drnevich, (1972b)“Shear Modulus and Damping in Soils: DesignEquations and Curves”, J. Soil Mech. FoundationsDiv. , V.98, pp.667–692.

Hatanaka, M., Y. Suzuki, T. Kawasaki, and M.Endo, (1988) “Cyclic Undrained Shear Properties ofHigh Quality Undistributed Tokyo Gravel”, Soil andFoundations, V.28, (No. 4), pp.57–68.

Ishihara, K. (1996) “Soil Behaviour in Earth-quake Geotechnics”, Oxford University Press, NewYork.

Katayama, I., F. Fukui, M. Satoh, Y. Makihara,and K. Tokimatsu, (1986) “Comparison of DynamicSoil Properties between Undisturbed and DisturbedDense Sand Samples”, Proc. 21st Annual Conf. ofJSSMFE, pp.583–584 (in Japanese).

Kawakami, H. and P. Bidon, (1997) “A Sim-plified Input Output Relation Method Using ARModel for Earthquake Wave Propagation Analysis”，Earthq. Engng. Struct. Dyn., V.26, pp.1041–1057.

Kawakami, H. and H. R. Haddadi, (1998)“Modeling Wave Propagation by Using Normal-ized Input-output Minimization (NIOM)”, Soil Dyn.Earthq. Engng., V.17, pp.117–126.

Langston, C. A., (1979) “Structure underMount Rainier, Washington, Inferred from Teleseis-mic Body Waves”, J. Geophys. Res., V.84, (No. B9),pp.4749–4762.

Ohta, Y., (1975) “Application of Optimiza-tion Technique into a Few Important Problems inEarthquake Engineering. Part 1: Estimation ofUnderground Structure at SMAC Site in HachinoheCity”, Transactions of the Architectural Institute ofJapan, V.229, pp.35–41 (in Japanese).

Seed, H. B., and I. M. Idriss, (1970) “SoilModuli and Damping Factors for Dynamic ResponseAnalyses”, Report no. EERC 70-10, Earthquake En-gineering Research Center, University of California,Berkeley, California.

Sun, J. I., R. Golesorkhi, and H. B. Seed,(1988) “Dynamic Moduli and Damping Ratios forCohesive Soils”, Report no. EERC 88-15, Earth-quake Engineering Research Center, University ofCalifornia, Berkeley, California.

Tokimatsu, K., H. Arai, and K. Minowa,(2008) “Soil Nonlinearity and Bedrock Strong Mo-tions Estimated from Downhole Array Records atKashiwazaki-Kariwa Nuclear Power Plant duringthe 2007 Niigata-ken Chuetsu-oki Earthquake”, J.Struct. Constr. Eng., V.73, (No. 630), pp.1273–1280(in Japanese).

Tokimatsu, K. and H. Arai, (2008) “NonlinearSoil Properties Estimated from Downhole ArrayRecordings at Kashiwazaki-Kariwa Nuclear PowerPlant in the Niigaka-ken Chuetsu-oki Earthquakes”,14th WCEE.

Tokyo Electric Power Company, Inc., (2008)“Accelerograms Observed at the Kashiwazaki-Kariwa Nuclear Power Plant (Revised version)”,DVD-ROM.

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