preliminary investigation for dynamic characteristics of great ...prev.enea.it/2013-12-12...

Dynamic Characteristics of Great Bronze Buddha of Kamakura

using microtremor

Yutaka NAKAMURA

System and Data Research, Tokyo JAPAN

Great Bronze Buddha of Kamakura Establishment: around AD 1250 Sitting Height: 11.4m Weight: 121 ton

The statue keeps almost original shape without massive repair. His hall was lost at 1369(?) by Tornado(?).

Tokyo

Yokohama

Kamakura

0 50 100 km

Location of Kamakura

Epicenters of Damaged Earthquakes after AD 5C

Kamakura

0 200 400 km

Seismic Environments of Kamakura

日本地震学会ホームページより引用・加工

Kamakura is located at high seismicity area in Japan.

My Interest: Why has not the Head

fallen down ?

Although receiving repeatedly strong motion after the establishment, the relatively large head has not fallen. Why? Nevertheless there is the weak point of neck connected between large head and body. How is the status of connection between the head and the body? I have investigated to clear the questions using microtremor measurement of statue itself and surrounding ground.

Measurement Points and the Situation

GN S4

GN S5

GN S6

GN S7

GN S8

G EW1

G EW2

G EW3

G EW4

GN S1

GN S2

GN S3

G EW5

Air view of measurement points in

the temple ground

図 2 大仏周辺の詳細測点配置

常時微動測点

ボーリング調査位置

柱石基礎

N

OG1

OG3

OG2

OG4

OG5

OG6 OG7 OG8 OG9 OG10

F1

F3

F2

F4

F5

F6 F7

F8

F9

F10

F11

F12

F13

IG1

IG3

IG2

IG4

IG5

IG6 IG7

IG8

IG9 IG10u IG11

IG12

IG13

IG14

IG15

IG16

IG17

IG18

IG19 IG21

IG22 IG20

IG10d

基壇 BT；N、NE、E、SE、S、、SW、W、 NW

基壇周床 BF；N。NE、E、SE、S、、SW、W、WB、NW

基壇 BT: N,NE,E,SE,S,SW,W, NW

基壇周辺床 BF: N,NE,E,SE,S,SW,W,WB, NW

Z0

Z1 Z2

Z4

Z3

X

Z

Y

N 常時微動測点

ボーリング調査位置

近傍柱石位置

＃1

＃2

＃3

＃4 ＃5

＃6

写真 1 地盤での微動測定

GNS6

写真 2 基壇上と周辺地盤

BFNW

BTNW

写真 3 大仏内背面窓での測定

DWR DWL

Measurement points around the Statue

First microtremor measurement was conducted at 2009-01-25, 26

On Ground Base and Ground Rear window in the Statue

図 4 高徳院境内（回廊外側）

測点の H/Vスペクトル比

増

幅

倍

率

振動数(Hz)

振動数(Hz) 振動数(Hz)

GNS1

0.1

1

10

0.1 1 10 100GNS2

0.1

1

10

0.1 1 10 100GNS3

0.1

1

10

0.1 1 10 100GNS4

0.1

1

10

0.1 1 10 100

GEW1

0.1

1

10

0.1 1 10 100GEW2

0.1

1

10

0.1 1 10 100

GNS5

0.1

1

10

0.1 1 10 100

GEW3

0.1

1

10

0.1 1 10 100GEW4

0.1

1

10

0.1 1 10 100

GNS6

0.1

1

10

0.1 1 10 100GNS7

0.1

1

10

0.1 1 10 100GNS8

0.1

1

10

0.1 1 10 100GEW5

0.1

1

10

0.1 1 10 100

Y方向

X方向

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

0.1

1

10

0.1 1 10 100

増

幅

倍

率

振動数(Hz) 振動数(Hz)

Z4:回廊外側

Z3:回廊内側

Z2:周辺石畳

Z1:基壇周辺

Z0:基壇上

(1)Ｘ方向 (2)Ｙ方向

図 5 回廊周辺 Z0～Z4での H/Vスペクトル比

Kg = A2/F g = Kg x a

Am

plif

icat

ion

Fac

tor

Frequency in Hz Frequency in Hz

Frequency in Hz

Am

plif

icat

ion

Fac

tor

Frequency in Hz Frequency in Hz X (EW) Component Y (NS) Component

Results of Microtremor Measurement

The HVSR for outside of cloister

The HVSR for around of cloister

Z4: outside

Z3: inside

Z2: stone pavement

Z1: around the base

Z0: on the base

Close to the statue

0 50m

Predominant Frequency F

Amplification Factor A

They show a distribution of predominant frequency and amplification factor estimated by HV spectral ratio derived from microtremor measurement. From A and F, Kg-value was estimated by this formula. The strain g

caused in surface layer is able to evaluate using Kg-value as this formula. a is peak ground acceleration PGA in Gal, cm/s2. Large Kg-value means vulnerable.

Stone Lantern: Damaged

Before the 3.11 Quake 2009-01-25

After the 2011.3.11 Quake K-net Kamakura Amax = 50Gal

Photo by Professor Sato ©2011Kotokuin

Kg of EW comp. Kg of NS comp.

W E

Bronze Lanterns and Flowers etc.:

Survived

Comparison Damage and Kg-value in case of the 3.11 Quake (Mw9.0)

N

S

Figures at right side show distribution of Kg-values in the temple. Kg-value of NS component is grater than EW component, and those of east side and south side are relative large. Microtremor measurement was conducted two years before the 2011 Tohoku Earthquake. Damage was recognized close to sites with large Kg-value. This photo is an example. Stone lantern near the site with large Kg-value was damaged, but bronze lanterns and flowers at lower Kg area were survived.

1

6

11

16

28

39

14

15

16

17

18

19

20

21

22

23

24

17 18 19 20 21 22 23 24 25 26 27

5

10

Y

X

40cm sliding

Kg values of Y-component (NS)

Strong motion at Kamakura by the 1923 event is estimated about 500Gal. Because maximum Kg is about 10, the shear strain caused in surface layer would be 5000m in maximum. Liquefaction might occurred. Before the liquefaction, the statue moved 40cm and pushed the stacked base stones by large strong motion. After the liquefaction the base sunk and behaved as natural base isolated device.

0

2

4

6

8

10N

NE

E

SE

S

SW

W

NW

0

2

4

6

8

10N

NE

E

SE

S

SW

W

NW

Kg_x

Kg_y

(a)基壇周辺地盤 (b)基壇

30cm sinking

Measurement Points for the

Statue

This microtremor measurement was conducted at 2013-07-23 to 25

: reference point for spectral analysis

Inner View

X

Y

2m

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DPL

DSL

DKL DKC

DRC

DFCC

DFFC

BFC

DPKL

DAC

DFR DFL

2m X

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL DKL DKC

DRC DFCC DFFC

BFC

DPKL

DAC

DFL DFR

2m Y

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL

DKL

DKC

DRC DFCC

DFFC

BFC

DPKL

DAC

DFL

DFR

図 1 測点配置

2mY

Z

0.1cm/s

2mX

Z

0.1cm/s

X

Y

2m0.1cm/s

図 4各部常時微動の速度軌跡

Rocking Vibration

X-Direction (Head)

Rocking Vibration

Y-Direction (Body)

Back Part of the Head

These Loci show the characteristics as follows;

On the body the motion of right-to-left direction is wholly same and that of front-to-back direction is mainly considered by rocking vibration. It suggests that the joints of the body are still healthy.

On the head, the motion shows more complex characteristics. Vibration of back of the head consists of mainly rocking vibration, and it shows the joint between the body and the back of the head is stable. On the other hand, the shapes of locus of the vibration at ear lobes and jaw show ellipse including vertical motion and it shows there is a problem with joint to the body.

It seems to be needed further investigation for joints of the head and between the head and the body.

Velocity Locus of each Point for 60 seconds

Amplification Characteristics of Sites against DRC

At the sites of the head under 10Hz vibrations are predominated. At the sites of the body over 10Hz vibrations are predominated. According to them, the body might be healthy but the connection between the head and the body and head Itself might have problems.

0.1

1

10

100

0.1 1 10 100

H2RCH2RC2DHLRCHLRC2DHRRCDELRCDERRCACRCACRC2ELRCELRC2ERRCERRC2

0.1

1

10

100

0.1 1 10 100

DUWRCDWLRCDWRRCUWRCSLRCSRRCUWRC1UWRC2UWRC3SRRC1

0.1

1

10

100

0.1 1 10 100

SWRC

KLRC

KCRC

KRRC

0.1

1

10

100

0.1 1 10 100

DPLRCDPRRCFLRCFRRCBFCRC

0.1

1

10

100

0.1 1 10 100


0.1

1

10

100

1000

0.1 1 10 100


0.1

1

10

100

0.1 1 10 100

SWRC

KLRC

KCRC

KRRC

0.1

1

10

100

1000

0.1 1 10 100


0.1

1

10

100

0.1 1 10 100


0.1

1

10

100

0.1 1 10 100


0.1

1

10

100

0.1 1 10 100

SWRC

KLRC

KCRC

KRRC

0.1

1

10

100

0.1 1 10 100


SRX（DRC を基準にしたスペクトル比） SRY（DRC を基準にしたスペクトル比）

SRZ（DRC を基準にしたスペクトル比）

振動数(Hz)

振動数(Hz)

振動数(Hz)

頭部

胴体上部

胴体下部

旧拝観台・基壇

頭部頭部

胴体上部胴体上部

胴体下部

胴体下部



増

幅

倍

率

図 5 DRC（後部床）を基準にした各部のスペクトル比（増幅特性）

Am

plif

icat

ion

Fac

tor

Frequency in Hz Frequency in Hz

Frequency in Hz

Spectral Ratios to DRC Spectrum

X-Component

Y-Component

Z-Component Platform/Base

Platform/Base

Platform/Base

Lower Body

Lower Body

Lower Body

Upper Body Upper Body Upper Body

Head Head Head

Mode Shapes of Predominant Frequencies for Y(NS)-Component

2m X

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL DKL DKC

DRC DFCC DFFC

BFC

DPKL

DAC

DFL DFR

2m Y

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL

DKL

DKC

DRC DFCC

DFFC

BFC

DPKL

DAC

DFL

DFR

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30

-1

0

1

2

3

4

5

6

7

8

9

10

0 50 100

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 100 200

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300

-1

0

1

2

3

4

5

6

7

8

9

10

0 50 100

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50

-1

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25

-1

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6

旧拝観台 1次 4.224Hz

X方向 Y方向

左右同相左右同相


X方向 Y方向

左右同相左右逆相


X方向 Y方向


X方向

卓越振動数

6.665Hz

Z方向

卓越振動数

4.224Hz

Z方向

卓越振動数

5.615Hz

Z方向

卓越振動数

7.568Hz

Z方向

卓越振動数

18.311Hz

Y方向

後頭部共振

5.737Hz

Y方向

顎部他共振

7.935Hz

Y方向

胴体下部共振

14.16Hz

D R C に対する増幅倍率

測

点

の

高

さ

（

ｍ

）

測

点

の

高

さ

（

ｍ

）

測

点

の

高

さ

（

ｍ

）

緑 7/23測定

灰 7/24測定

橙 7/25測定

後頭部耳朶部顎部上窓窓下旧拝観台印相部他床部

R L

図 6 さまざまな卓越振動数に対する振動モード（DRCに対する増幅倍率分布）

Hei

ght

of

Mea

sure

me

nt

Poin

t in

m

Y-Comp. Predominant Frequency



measured

measured

measured

Head Ear Lobe

Jaw

Upper Window

Platform

Lower Window

Floor

Hand etc.

It can be seen two predominant vibrations for front-to-back motion of the head. The vibration around 7.9Hz resonates at the ear lobes and the jaw and has an effect on the body. And that around 5.7Hz resonates at the back of the head. Difference of the vibration characteristics between front and back of the head must be noticed because it relates to healthy of the head.

Amplification Factor against DRC

Mode Shapes of Predominant Frequencies for X(EW) and Z(UD) Components

2m X

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL DKL DKC

DRC DFCC DFFC

BFC

DPKL

DAC

DFL DFR

2m Y

Z

DSW

DKR

DPR

DWR

DER

DBHR

DSR

DPKR

DBHL

DBH2R

DEL

DWL

DUWL

DPL

DSL

DKL

DKC

DRC DFCC

DFFC

BFC

DPKL

DAC

DFL

DFR

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30

-1

0

1

2

3

4

5

6

7

8

9

10

0 50 100

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 100 200

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20

-1

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300

-1

0

1

2

3

4

5

6

7

8

9

10

0 50 100

-1

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50

-1

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25

-1

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6


X方向 Y方向

左右同相左右同相


X方向 Y方向



X方向 Y方向


X方向

卓越振動数

6.665Hz

Z方向

卓越振動数

4.224Hz

Z方向

卓越振動数

5.615Hz

Z方向

卓越振動数

7.568Hz

Z方向

卓越振動数

18.311Hz

Y方向

後頭部共振

5.737Hz

Y方向

顎部他共振

7.935Hz

Y方向

胴体下部共振

14.16Hz

D R C に対する増幅倍率

測

点

の

高

さ

（

ｍ

）

測

点

の

高

さ

（

ｍ

）

測

点

の

高

さ

（

ｍ

）

緑 7/23測定

灰 7/24測定

橙 7/25測定

後頭部耳朶部顎部上窓窓下旧拝観台印相部他床部

R L

図 6 さまざまな卓越振動数に対する振動モード（DRCに対する増幅倍率分布）

Amplification Factor against DRC Hei

ght

of

Mea

sure

me

nt

Poin

t in

m

Z-Comp. Predominant Frequency




X-Comp. Predominant Frequency

The right-to-left vibration predominates around 6.7Hz and resonates at the head, especially at the back of the head. The vertical motion resonates at 5.6Hz and 7.6Hz at the ear lobes and the jaw, and resonates relative higher frequency at 18.3Hz at the back of the head.

From these results, it seems that the head has a problem at the ear lobes and the jaw rather than at back of the head.

Concluding Remarks During strong motion: *Because the statue slide on the base, and *Because the basement ground under the base liquefied, the statue itself did not received such a strong motion.

They can be thought that these are caused by natural seismic isolation system.

At the time of the retrofitting 50 years ago, the bottom of the statue was reinforced with concrete perimeter beams. And a 3mm-thick stainless sheet was attached to the bottom of the perimeter beams and a granite plate with smoothed surface was covered over the base to contact the stainless sheet. This was designed to keep the safety of the statue itself with sliding the statue on the base during strong motion.

This is the first seismic isolation system applied to cultural property in Japan, and it is necessary to investigate the system still working and to conduct countermeasure against front base sinking when strong motion attacked.

*The joint between the head and the body shows a different aspects between front and back sides and right and left sides.

It is necessary to conduct deep investigation especially for the head to complete the countermeasure against earthquake hazard.

Upper surface of Podium filled by Granite Planks with smoothed surface

rimed with Copestones

Stainless steel sheet with stud to fix bottom side of RC Beam

RC Beams to reinforce the open-end bottom of the statue

Rigid frame on RC Beam to

support the upper load

This investigation was conducted under the committee of repair for Great Buddha of Kamakura. I’d like to express my deepest appreciation to committee and relations.

Thank you for your kind attention

preliminary investigation for dynamic characteristics of great ...prev.enea.it/2013-12-12...

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