dynamic characteristics of the colosseum at the pillar #40 ... · t kuh first modes of the pillar...

_______________________________

1 System and Data Research, Tokyo, Japan

2 University of l’Aquila, Italy

1

Dynamic Characteristics of the Colosseum at

the Pillar #40 Comparing the Results of

Microtremor Measurement in 1998 and 2013 Yutaka Nakamura1, Jun Saita1, Tsutomu Sato1 and

Gianfranco Valente2

Abstract Our first near full-scaled microtremor measurement at Colosseum

was in 1998, and we had an opportunity to measure again near the pil-

lar #40 in 2013 at almost the same point of that of the past measure-

ment. Here, the results of the measurement in 1998 and 2013 at the

pillar #40 can be compared. As a result, both spectral shapes agree

well in wide frequency range. However confirming the detail of the

predominant frequency and the amplification factor, they slightly dif-

fer for each other. The result of measurement in 2013 shows that the

peaks shifts to a little higher in radial direction and lower in circum-

ferential direction, and the amplification factor becomes larger for

each direction. And the mode changing the phase for 180 degrees be-

tween 3F and 4F can be commonly observed in 1998 but not in 2013.

There seems to be something structural difference between 3F and 4F,

for example the affection of the 2009 L’Aquila earthquake or the work

of the floors and the fences of 4F and 3F in 2010. If the degradation of

the structure can be grasped quantitatively with periodic microtremor

measurement, it is possible to maintain rationally and is not impossi-

ble to take a countermeasure as reinforcement of maintenance prophy-

lactically and properly. It is necessary for establishing the method for

applying to confirm the accuracy of the microtremor measurement,

and to make clear the reason of changing the dynamic characteristics

at pillar #40 quantitatively.

Dynamic Characteristics of the Colosseum at the Pillar #40 Comparing the Results of Measurement in 1998 and 2013 Y. Nakamura, J. Saita, T. Sato and G. Valente

System and Data Research

Dynamic Characteristics of the

Colosseum at the Pillar #40

Comparing the Results of

Measurement in 1998 and 2013

Yutaka NAKAMURA1), Jun Saita1), Tsutomu Sato1),

and Gianfranco Valente2)

1) System and Data Research, Tokyo, Japan.

2) L’Aquila University, L’Aquila, Italy

North

South

Starting Construction: around 75AD

Completion: 80AD

Size: major axis 188m, minor axis 156m and height 48m

Capacity: approximately 50,000 peoples

Foundation: spread foundation, thickness 12m

Upper Structure: inner ring is survived almost completely,

outer ring is survived only northern half.


Outline of Colosseum


INTRODUCTION

Our first near full-scaled microtremor measurement at

Colosseum was in 1998, and we had an opportunity

to measure again near the pillar #40 in 2013 at almost

the same point of that of the past measurement.

Here, the results of the measurement in 1998 and

2013 at the pillar #40 can be compared.


Locations of Microtremor Measurement

2013

This is the distribution of the past measurement

points. Red line indicates the location of pillar #40.

1st Floor

25

26

27

28

24

29

30

31

32

33

34

35

36

373839404142434445

46

47

48

49

50

56

57

58

59

51

53

54

55

52

69

70

71

60

61

6263

64

6566

6768

72

3 4

5

6 7

8

910

1 2

73 74 75 76 77 78 79 80

16

17

20

21

22

23

1112

13

14

15

18

19

25

26

27

28

24

29

30

31

32

33

34

35

36

373839404142434445

46

47

48

49

50

56

57

58

59

51

53

54

55

52

69

70

71

60

61

6263

64

6566

6768

72

3 4

5

6 7

8

910

1 2

73 74 75 76 77 78 79 80

16

17

20

21

22

23

1112

13

14

15

18

19

25

26

27

28

24

29

30

31

32

33

34

35

36

373839404142434445

46

47

48

49

50

56

57

58

59

51

53

54

55

52

69

70

71

60

61

6263

64

6566

6768

72

3 4

5

6 7

8

910

1 2

73 74 75 76 77 78 79 80

16

17

20

21

22

23

1112

13

14

15

18

19

0 50 100 m

Column Number

Column N

umber

Colum

n Num

ber

2nd Floor

3rd ( ) and 4th (

) Floors

1F1

1F3

1F3I

I

1F4I

I

1F2

: Measurement at Nov. 1997 ○: Measurement at July 1998

Figure 1. Distribution of Measuring Points for Colosseum in Rome (3)

1997 1998

Measurement points for 2013 (small greens are measured in 1998)

Monument

North

0 10 20 30 40 50m

Pillar #40

2013


GF 2013

GF 1998

4F This point was measured at 2013,

but no mention in this report

3F

2F

1F

Measurement Locations along Pillar #40

Points 1F to 4F were measured at 2013 and 1998.

Z

T R

Locations of Microtremor Measurement

This figure shows the

measurement points

related to the pillar #40.

Microtremor measured at

almost same points both in

1998 and 2013 without the

ground floor.


Situation of Sites 4F

2013Dec.

3F

2013Dec.

2F

2013Dec. 1F

2013Dec.

GF

2013Dec. 1998July

GF

1998J

uly

1F

1998J

uly

2F

1998J

uly

3F

1998J

uly

4F

Measurement points at pillar #40 of Colosseum in 2013 and 1998

Red circles: sensor location, Green triangle: sensor location of 2013

GF

2013

GF

1998

4F This point was measured at 2013,

but no mention in this report

3F

2F

1F

Measurement Locations along Pillar #40

Points 1F to 4F were measured at

2013 and 1998.

Z

T R

These pictures show the situation the points

related to the pillar #40. Left side and right side

corresponds to the measurement in 2013 and

1998, respectively. The picture of the points in

1998 shows them in 2013 as green triangles.

From this, the points locate almost same place.


Comparison of the Amplification Spectra of Pillar #40

evaluate from measurements in 1998 and 2013

0.1

1

10

100

1 10

4F

3F

2F

1F

#40R1998

0.1

1

10

100

1 10

4F

3F

2F

1F

#40R2013

0.1

1

10

100

1 10

4F

3F

2F

1F

#40T1998

0.1

1

10

100

1 10

4F

3F

2F

1F

#40V1998

0.1

1

10

100

1 10

4F

3F

2F

1F

#40T2013

0.1

1

10

100

1 10

4F

3F

2F

1F

#40V2013

Frequency in Hz Frequency in Hz Frequency in Hz

This slide compares the amplification spectrum of the pillar #40 between the measurement

in 1998 and 2013 for each direction. Each spectral shapes agree well in wide frequency

range. However confirming the detail of the predominant frequency and the amplification

factor, they slightly differ for each other.

radial component

radial component

vertical component

vertical component

Tangential component

Tangential component 2013 2013 2013

1998 1998 1998


Predominant Frequencies, its Amplification and

Kb-Values for the Pillar #40 of Colosseum 2013 Height(m) Tangential Radial Vertical

Predom. Fre. (Hz) 2.661 1.733 13.330 between Height(m)

4F 37.5 16.7 23.9 7.3 4F and 3F 34.79 2.4 98.5 0.20

3F 32.08 16.3 17.5 6.5 3F and 2F 28.02 19.5 75.7 0.30

2F 23.96 11.9 10.3 4.8 2F and 1F 18.215 19.0 51.4 0.28

1F 12.47 5.8 3.2 2.5 1F and GF 6.235 13.8 15.2 0.18

GF 0.0 1.0 1.0 1.0

1998 Height(m) Tangential Radial Vertical

Predom. Fre. (Hz) 2.905 1.685 10.547 between Height(m)

4F 37.5 14.1 18.5 5.3 4F and 3F 34.79 8.1 71.3 0.16

3F 32.08 12.7 14.1 5.0 3F and 2F 28.02 12.5 61.9 0.26

2F 23.96 9.3 8.5 4.0 2F and 1F 18.215 12.2 42.8 0.35

1F 12.47 4.6 3.0 2.3 1F and GF 6.235 8.7 14.4 0.24

GF 0.0 1.0 1.0 1.0

Vertical

Tangential Radial Vertical

Table 1. Predominant Frequencies, its Amplification and Kb values for Column #40 of Colosseum

Kbi (m/Gal)

Kbi (m/Gal)

Amplificationagainst GF

Amplificationagainst GF

Tangential Radial


HkT

First Modes of the Pillar #40 of Colosseum

0

5

10

15

20

25

30

35

40

0 5 10 15 20

Tangential

0

5

10

15

20

25

30

35

40

0 10 20 30

Radial

0

5

10

15

20

25

30

35

40

0 2 4 6 8

Vertical

Heig

ht

inm

コロッセオ#40柱の1次モード

1998 19981998

20132013

2013

Amplification Factor Amplification Factor Amplification Factor

2.661 Hz

2.905 Hz

1.733 Hz

1.685

Hz

13.330Hz

10.547Hz

40T 40R 40Z

This slide shows a graphic representation of the table before. The result of measurement

in 2013 shows that the peaks shifts to a little higher in radial direction and lower in

tangential direction, and the amplification factor becomes larger for each direction.


Animation of Mode Shape

This animation shows the amplification mode of each direction continuously over the figure

comparing the amplification spectrum before. Blue and green indicate the result of 2013 and

1998, respectively. And this shows the vibration mode of one cycle by every 10 degrees.


A Difference between 1998 and 2013

The mode changing the phase for 180 degrees between 3F and

4F can be commonly observed in 1998 but not in 2013. There

seems to be something structural difference between 3F and 4F.


Corresponding

bricks: there are

lacks of bricks

4F

2013Dec.

4F

1998July.

2013-12-13

1998-07-06

What is change?

This slide makes

clear the changing

situation from the

documentary

photographs etc.

This compares the

situation of 4F.

At first the joint of the floor is changed and the shape of the fence is also changed.


What is change?

2013-12-13

Lower photograph in enlarged

picture shoot at the time of the

2013 measurement and we

can see something like a

drainpipe not existed before.

Upper photograph shows the comparison of

the floor of 4F by Google Earth. The joint in

a concentric fashion seen before cannot be

recognized.

20070729 by GoogleEarth


This photo taken at 2010-11-24 from web

2010-03-20

Old Fence

When?

2010-11-24

New Fence


HkT

The change of First Modes of the Pillar #40

0

5

10

15

20

25

30

35

40

0 5 10 15 20

Tangential

0

5

10

15

20

25

30

35

40

0 10 20 30

Radial

0

5

10

15

20

25

30

35

40

0 2 4 6 8

VerticalH

eig

ht

inm

コロッセオ#40柱の1次モード

1998 19981998

20132013

2013

Amplification Factor Amplification Factor Amplification Factor

2.661 Hz

2.905 Hz

1.733 Hz

1.685

Hz

13.330Hz

10.547Hz

40T 40R 40Z

R

T

1998

2013

These changes of the structural characteristics are harmonic to the change of the

microtremor characteristics, and it is expected to capture the change of the structural

characteristics by monitoring the microtremor characteristics.


dj: Displacement at jth Floor

dj = Ajag/wn2

= Ajag/(2pfn)2

gj: Drift Angle at jth Layer

gj = (Aj – Aj-1)/hj/(2pFn)2ag

= Kbjag

Kbj = (Aj – Aj-1)/hj/(2pFn)2

ag: PGAAj: Amplification Factor at jth FloorFn: Natural Frequency of the Buildinghj: Height of jth Layer

A

A

A1st Floor

nth Floor

jth Floor

Ground Floorg1

gj(j-1)th Floor hj

Seismic Acceleration ag

dj

Large K-value means that the portion is vulnerable.

On the Kb-value <a Destructive Index>

Please see the detail of Kb value on reference below as a name of KT. => Nakamura, Y. and et al.(2000):

Vulnerabiliy Investigation of Roman Collisseum using Microtremor, 12th WCEE, paper #2660.

This is

explanation of Kb-

value. It can be

used for

estimation of drift

angle for each

floor by Kb-value

times PGA, peak

ground

acceleration.


Kb-Values Distribution for First Mode of the Pillar #40

0

5

10

15

20

25

30

35

40

0 10 20 30

Tangential

0

5

10

15

20

25

30

35

40

0 50 100 150

Radial

0

5

10

15

20

25

30

35

40

0 0.1 0.2 0.3 0.4

Vertical

1998

1998 1998 201320132013

Kb value (m/Gal) Kb value (m/Gal) Kb value (m/Gal)

コロッセオ#40柱の1次モードに対応するKb値分布

40T 40R 40Z

Heig

ht

inm

The Kb value in 2013 becomes larger in almost all the direction than that in 1998, and it

indicates that the structure has weakened. Especially the value becomes 1.4 times against

that in 1998 for the radial direction and the story drift at the pillar of 3F is estimated to reach

1% by the earthquake motion about 100 Gal.


CONCLUSIONS-1

The shape of the transfer function agrees basically in wide frequency

range for the three directions by comparing the measurement result in

1998 and 2013. However, the predominant frequency and amplification

factor slightly differ each other.

The predominant frequency of 2013 shifted rather higher than that of

1998 for the radial direction and lower than that of 1998 for the tangential

direction. And the amplification factor becomes large for each direction.

In the animation, we can see a mode changes the phase 180 degrees

between 3F and 4F in 1998 for the radial direction with growing

predominant frequency, however this mode cannot be recognized in 2013.

This suggests that there is some structural change between 3F and 4F

during the period from 1998 to 2013.


CONCLUSIONS-2 Actually a renewal work of fences and floors at 3F and 4F in 2010, and

the joint of the floor was changed. These changes agree with that of

microtremor characteristics and it shows the possibility to grasp the

structural change with monitoring microtremor.

The Kb value in 2013 becomes larger in almost all the direction than that

in 1998, and it indicates that the structure has weakened. Especially the

value becomes 1.4 times against that in 1998 for the radial direction and

the story drift at the pillar of 3F is estimated to reach 1% by the

earthquake motion about 100 Gal.

It is important for reinforcement of Colosseum to grasp the effect of

reinforcement quantitatively. And it requests a measurement before

and after the reinforcement, and it is necessary to investigate the

reason on the change of the characteristics at pillar #40 because of

confirming the availability of the measurement.


Acknowledgements

The measurement in Colosseum is greatly attributed to the heavy work done by Prof.

Antonio Rovelli of INGV, Dr. Paolo Clemente of ENEA. And Ms. Cinzia Conti of

Soprintendenza speciale per i Beni Archeologici di Roma and other concerned

personnel gave admissions agreeably and full facilities to our measurement.

I greatly appreciate their help.

Thank you for your attention.

dynamic characteristics of the colosseum at the pillar #40 ... · t kuh first modes of the pillar...

Documents