Dynamic Characteristics of the Colosseum at the Pillar #40 Comparing the Results of Microtremor Measurement in 1998 and 2013

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1 Dynamic Characteristics of the Colosseum at the Pillar # Comparing the Results of Microtremor Measurement in and Yutaka Nakamura 1, Jun Saita 1, Tsutomu Sato 1 and Gianfranco Valente 2 Abstract Our first near full-scaled microtremor measurement at Colosseum was in, and we had an opportunity to measure again near the pillar # in at almost the same point of that of the past measurement. Here, the results of the measurement in and at the pillar # 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 differ for each other. The result of measurement in shows that the peaks shifts to a little higher in radial direction and lower in circumferential direction, and the amplification factor becomes larger for each direction. And the mode changing the phase for 180 degrees between 3F and 4F can be commonly observed in but not in. There seems to be something structural difference between 3F and 4F, for example the affection of the 09 L Aquila earthquake or the work of the floors and the fences of 4F and 3F in. If the degradation of the structure can be grasped quantitatively with periodic microtremor measurement, it is possible to maintain rationally and is not impossible to take a countermeasure as reinforcement of maintenance prophylactically 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 # quantitatively. 1, Tokyo, Japan 2 University of l Aquila, Italy 1

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

3 Dynamic Characteristics of the Colosseum at the Pillar # Comparing the Results of Measurement in and Yutaka NAKAMURA 1), Jun Saita 1), Tsutomu Sato 1), and Gianfranco Valente 2) 1), Tokyo, Japan. 2) L Aquila University, L Aquila, Italy

Outline of Colosseum North South Starting Construction: around 7AD Completion: 80AD Size: major axis 188m, minor axis 6m and height 48m Capacity: approximately

4 Outline of Colosseum North South Starting Construction: around 7AD Completion: 80AD Size: major axis 188m, minor axis 6m and height 48m Capacity: approximately 0,000 peoples Foundation: spread foundation, thickness 12m Upper Structure: inner ring is survived almost completely, outer ring is survived only northern half.

5 INTRODUCTION Our first near full-scaled microtremor measurement at Colosseum was in, and we had an opportunity to measure again near the pillar # in at almost the same point of that of the past measurement. Here, the results of the measurement in and at the pillar # can be compared.

61 61 61 41 41 41 2 2 2 3 3 3 4 4 4 7 8 9 60 7 8 9 60 7 6 6 6 62

Microtremor Measurement 1 1 67 1 67 0 68 68 0 0 69 69 49 49 49 70

43 43 77 42 42 78 Column Number 39 39 38 38 37 3 rd ( ) and 4th (

3 3 3 7 34 34 34 8 33 33 33 9 32 32 32 11 11 1997 31 31 31 12 12

23 22 18 23 22 18 27 27 21 19 21 19 27 26 26 Column Number 26 24

(small greens are measured in ) 9 60 8 62 63 64 6 66 71 72 73 74 7

13 14 70 11 71 72 73 74 7 76 77 78 79 80 1F4I 1 1 st Floor 6 7 8 9

Distribution of Measuring Points for Colosseum in Rome (3) This is

6 F1 Locations of Microtremor Measurement Column Number rd ( ) and 4th ( ) Floors 42 2 nd Floor m 79 1F Column Number Column Number Pillar # m Monument North Measurement points for (small greens are measured in ) F3I 1F F4I 1 1 st Floor : Measurement at Nov : Measurement at July Figure 1. Distribution of Measuring Points for Colosseum in Rome (3) This is the distribution of the past measurement points. Red line indicates the location of pillar #.

GF 1F GF Measurement Locations along Pillar # This figure shows the measurement

7 Locations of Microtremor Measurement R 4F This point was measured at, but no mention in this report Z T 3F 2F Points 1F to 4F were measured at and. GF 1F GF Measurement Locations along Pillar # This figure shows the measurement points related to the pillar #. Microtremor measured at almost same points both in and without the ground floor.

8 Measurement points at pillar # of Colosseum in and Red circles: sensor location, Green triangle: sensor location of 4F Dec. 3F Dec. 2F Dec. 1F Dec. GF Dec. J uly 3F J uly 1F J uly 4F J uly 2F July GF GF Situation of Sites Measurement Locations along Pillar # 4F This point was measured at, but no mention in this report 3F 2F 1F GF Points 1F to 4F were measured at and. These pictures show the situation the points related to the pillar #. Left side and right side corresponds to the measurement in and, respectively. The picture of the points in shows them in as green triangles. From this, the points locate almost same place. R Z T

9 Comparison of the Amplification Spectra of Pillar # evaluate from measurements in and 0 4F 3F 2F 1F #T 0 #R 4F 3F 2F 1F 0 4F 3F 2F 1F #V Tangential component 1 radial component vertical component 1 0 4F 3F 2F 1F #T 0 #R 4F 3F 2F 1F 0 4F 3F 2F 1F #V 1 Tangential component radial component vertical component Frequency in Hz Frequency in Hz Frequency in Hz This slide compares the amplification spectrum of the pillar # between the measurement in and 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.

10 Predominant Frequencies, its Amplification and Kb-Values for the Pillar # of Colosseum Height(m) Tangential Radial Vertical Predom. Fre. (Hz) between Height(m) Amplification against GF 4F F and 3F F F and 2F F F and 1F F F and GF GF Height(m) Tangential Radial Vertical Predom. Fre. (Hz) between Height(m) Amplification against GF Table 1. Predominant Frequencies, its Amplification and Kb values for Column # of Colosseum 4F F and 3F F F and 2F F F and 1F F F and GF GF Kbi (m/gal) Kbi (m/gal) Tangential Radial Vertical Tangential Radial Vertical

11 Height in m T k H 3 30 First Modes of the Pillar # of Colosseum Tangential コロッセオ # 柱の 1 次モード 3 Radial T R Z 2.90 Hz Hz Hz Hz 3 30 Vertical.47Hz Hz Amplification Factor Amplification Factor Amplification Factor This slide shows a graphic representation of the table before. The result of measurement in 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.

12 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 and, respectively. And this shows the vibration mode of one cycle by every degrees.

13 A Difference between and The mode changing the phase for 180 degrees between 3F and 4F can be commonly observed in but not in. There seems to be something structural difference between 3F and 4F.

14 This slide makes clear the changing situation from the documentary photographs etc. This compares the situation of 4F. What is change? 4F Dec. Corresponding bricks: there are lacks of bricks 4F July At first the joint of the floor is changed and the shape of the fence is also changed.

15 by GoogleEarth What is change? Upper photograph shows the comparison of the floor of 4F by Google Earth. The joint in a concentric fashion seen before cannot be recognized. Lower photograph in enlarged picture shoot at the time of the measurement and we can see something like a drainpipe not existed before.

16 When? -03- Old Fence New Fence This photo taken at from web

Height in m T k H 3 30 The change of First Modes of the Pillar # Tangential コロッセオ # 柱の 1 次モード 3 Radial T R Z 2.90 Hz 30 1.

330Hz 0 0 0 0 0 30 0 2 4 6 8 Amplification Factor Amplification Factor Amplification Factor T These changes of the

17 Height in m T k H 3 30 The change of First Modes of the Pillar # Tangential コロッセオ # 柱の 1 次モード 3 Radial T R Z 2.90 Hz Hz Hz Hz 3 30 Vertical.47Hz R Hz Amplification Factor Amplification Factor Amplification Factor T 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.

18 On the K b -value <a Destructive Index> n th Floor j th Floor (j-1) th Floor 1 st Floor Ground Floor A A A h j Seismic Acceleration a g d j g 1 g j d j : Displacement at j th Floor g j : Drift Angle at j th Layer d j = A j a g /w n 2 = A j a g /(2pf n ) 2 g j = (A j A j-1 )/h j /(2pF n ) 2 a g = K bj a g K bj = (A j A j-1 )/h j /(2pF n ) 2 a g : PGA A j : Amplification Factor at j th Floor F n : Natural Frequency of the Building h j : Height of j th Layer Large K-value means that the portion is vulnerable. This is explanation of Kbvalue. It can be used for estimation of drift angle for each floor by Kb-value times PGA, peak ground acceleration. Please see the detail of K b value on reference below as a name of K T. => Nakamura, Y. and et al.(00): Vulnerabiliy Investigation of Roman Collisseum using Microtremor, 12th WCEE, paper #2660.

19 Height in m コロッセオ Kb-Values Distribution # 柱の1 次モードに対応する for First Mode of the Pillar Kb 値分布 # 3 30 Tangential 3 30 Radial 3 30 Vertical T R Z Kb value (m/gal) Kb value (m/gal) Kb value (m/gal) The Kb value in becomes larger in almost all the direction than that in, and it indicates that the structure has weakened. Especially the value becomes 1.4 times against that in for the radial direction and the story drift at the pillar of 3F is estimated to reach 1% by the earthquake motion about 0 Gal.

20 CONCLUSIONS-1 The shape of the transfer function agrees basically in wide frequency range for the three directions by comparing the measurement result in and. However, the predominant frequency and amplification factor slightly differ each other. The predominant frequency of shifted rather higher than that of for the radial direction and lower than that of 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 for the radial direction with growing predominant frequency, however this mode cannot be recognized in. This suggests that there is some structural change between 3F and 4F during the period from to.

21 CONCLUSIONS-2 Actually a renewal work of fences and floors at 3F and 4F in, 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 becomes larger in almost all the direction than that in, and it indicates that the structure has weakened. Especially the value becomes 1.4 times against that in for the radial direction and the story drift at the pillar of 3F is estimated to reach 1% by the earthquake motion about 0 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 # because of confirming the availability of the measurement.

22 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 Comparing the Results of Microtremor Measurement in 1998 and 2013

Dynamic Characteristics of the Colosseum at the Pillar #40 Comparing the Results of Microtremor Measurement in 1998 and Yutaka Nakamura 1, Jun Saita 1 and Tsutomu Sato 1 Abstract Our first extensive microtremor