Dynamic Characteristics of Memorial Columns ofTrajan and Marcus Aurelius using Microtremor
Yutaka Nakamura1, Jun Saita1 and Tsutomu Sato1

Abstract
Memorial Columns of Trajan (TC) and Marcus Aurelius (AC) in
Rome with a similar structure and size were studied their dynamic
characteristics by microtremor measurement. As a result, thefundamental frequencies of horizontal vibration are approximately 1.6
Hz for TC and 1.3 Hz for AC, and caused mainly by bending vibration.
These agree with the result of the previous investigation. Predominantfrequencies of torsion and longitudinal vibrations are estimatedapproximately 15.5 Hz and 25.6 Hz, respectively. From these values
the propagation velocities of shear wave and longitudinal vibration are
estimated as 1900 m/s and 3100 m/s, respectively. Although thesevalues are relatively small, about 65% of typical value, Poisson's ratio
is estimated reasonable value about 0.33. On the other hand, thepredominant frequencies of the torsional and longitudinal vibrations ofAC are approximately 9.1 Hz and 18.8 Hz, respectively, and thevelocity of shear wave and longitudinal vibration are estimatedconsiderably low value as 1100 m/s and 2300 m/s, respectively.
Longitudinal vibration propagation velocity is more than 50% lower
than typical value, and the shear wave velocity is too low to estimate
Poisson's ratio. It seems to be caused by low natural frequency of
torsional vibration, and it is observed a tightened up vertical longdamage on the west side of column body causing low registanceagainst torsional vibration. The destructive index Kb-value of thecolumns derived from the fundamental mode of bending vibration is
83 μ/Gal in maximum for upper part of TC and is 212 μ/Gal for top of
AC with large variation. Thus, drift angle over 1/120 radian will becaused about 100 Gal of earthquake motion at base ground for TC andlower than 50 Gal of earthquake motion for AC.
_______________________________
1 System and Data Research, Co., Ltd., Tokyo, Japan

Yutaka Nakamura, Jun Saita and Tsutomu Sato2

1. Introduction
Memorial Columns of Trajan and Marcus Aurelius (referred as TC
and AC hereafter) in Rome had been completed with same structureand size in 113 AD and 193 AD, respectively. Cylindrical surface ofeach column has spiral relief. Each memorial columns consist of
stacked marble blocks hollowing out spiral staircase and each block isapproxicimately 3.6m diameter and 1.52m height in average and hashollowed out 8 steps spiral staircase. Totally 19 blocks including
terrace and base of the column are layered for approximately 30m
height with two blocks for stature base on terrace. Figure 1 showsmodels of staircase and block. Their foundation grounds are hard for
TC and relatively soft for AC. AC has been received severe damage of
weathering and earthquakes, and massive restoration has been done already in the 16th century. Although TC was made earlier than AC andImage Model of
Spiral Staircase in
Columns

Trajan’s Column

MarcusAurelius’s
Column

Plaster Cast Miniature of
the Marble Block
Figure 1. Models of Spiral Staircase and BlockDynamic Characteristics of Memorial Columns

3

has been received the weathering and artificial damages, it still remains almost original form in present.
There have been research works on dynamic characteristics of TC
and AC previously, and our research aims to grasp precisely theexisting condition and reports the result of the preliminary
microtremor measurement for both TC and AC.

2. Microtremor Measurement and Data Analysis
The measurements were done between 10 a.m. to 2 p.m. at 28th
March of 2012, TC in the morning and AC in the afternoon. The
weather was fine. Figure 2 shows the distribution of the measuring
points for TC and AC, indicating for under the terrace and spiral staircase without accuracy in dimension.
For TC there are five measurement points, TTN, TTE, TTS, TTW
and TTC on the terrace, the highest floor. Two couples of measurement points, TTN-TTS and TTE-TTW, were measured simultaneously for detecting rocking and torsional vibration. Also four points on
surface ground, TBN, TBE, TBS and TBW were set with contacting
the pedestal, and two couples of measurement points, TBN-TBS and
TBE-TBW, were measured simultaneously. For measurement of column body, one continuous measuring point TTC, inside of the entrance on east side of the terrace, was set for simultaneous measurement. The spiral staircase of TC turns one rotation by 14 steps. From
TTC, four points, TC1 to TC4, were set every 28 steps, and otherthree points, TC45, TC5 and TC6 were set every 14 steps in the column body, and TC7 five steps under TC6 were set in the pedestal.
For AC, all the measuring points were measured individually. Fivepoints, MTN, MTE, MTS, MTW and MTC on the terrace, under the
MTC, six points of MT1 to MT6 were set every 28 steps, and MT7
and MT8 were set 22 steps and 36 steps under the MT6 respectively.
The spiral staircase of AC has 14 steps per turn as same as TC. At
each point, microtremor of three components EW, NS and UD were
measured simultaneously for duration of three minutes with 1/100
seconds sampling.

Yutaka Nakamura, Jun Saita and Tsutomu Sato

4

MC
MTS

TTN

Plan North for TC

MTE

TTE

MTC MTW

TTC

MTN ①

TTS
TTW

①
②

②
③

③
MC1

TC1
④

④

⑤

⑤
⑥

⑥
TC2 ⑦

⑦
MC2
⑧

⑧
⑨

slippage joint

⑨
⑩

⑩
MC3

TC3
⑪

⑪

⑫

⑫

⑬

⑬
⑭

⑭
TC4
TC4

Plan North for TC

Trajan's
Columnpoint steps
TTN 185
TTE 185
TTS 185
TTW 185
TTC 185
TC1 157
TC2 129
TC3 101
TC4 73
TC45 59
TC5 45
TC6 31
TC7 26
TBN
0
TBE
0
TBS
1
TBW
0

MC4

⑮

MC4
⑮

⑯

⑯
TC45

⑰

⑰
MC5

⑱
う
⑲

TC5
⑱
う
⑲
TC6

TC7

MC6

TBE
MC7

TBS

TBN

MarcusAurelius's
Columnpoint steps
MTN 190
MTE 190
MTS 190
MTW 190
MTC 190
MC1 162
MC2 134
MC3 106
MC4 78MC5 50MC6 22MC70
MC8 -14TBW(1) Trajan’s Column

MC8
MC8

*MC8 より下には螺旋階段はなく、
狭Ｃ８(2) Marcus Aurelius’s Column

く複雑な地下空間が拡がっているよ
うにみえた。

Figure 2. Distribution of the Points
for Microtremor Measurements*ブロック⑩と⑪の継目部分（赤）の表面レリーフは、8.2cm ずれている。

Dynamic Characteristics of Memorial Columns

5Frequency analysis has been carried out by Fourier transform forthe measured waveform. The response spectra of TC and AC have been
estimated using simultaneous and individual measurement, respectively.
The analysis used 40.96 seconds (4096 data) length record and thefinal result was derived spectra averaged three or four times. Also thespectral ratio of target point against base point or H/V spectral ratio isderived. These results of individual or simultaneous measurement arecompared and investigated.

3. Result of Analysis
3.1. Column of Trajan
Table 1 shows the results of the analysis of the predominant fre1. Resultsof Microtremor
Measurement
TC
Table 1.Table
Resultsof Microtremor
Measuements
forofTC
TC
Simultaneous.
F Hz
maxAF maxKb/Kg
EW
1st
1.59
18.8
83.1
2nd
8.99
7.8
5.0
3rd
19.17
6.3
1.2
NS
1st
1.59
15.5
77.2
2nd
8.99
5.2
3.4
3rd
20.29
9.3
1.0
Longitudinal
1st
25.64
7.8
0.2
TorsionalTC

1st
Individual

15.53
F

Hz

maxAF

EW

1st

1.59

188.8

NS

2nd
3rd
1st
2nd
3rd

9.03
19.04
1.59
9.03
20.26

8.3
6.0
98.6
7.3
9.6

H/V

F Hz

maxAF

EW

1st

1.51

22.0

NS
Ground: BN
BE
BS
BW

1st
1st
1st
1st
1st

1.44
5.81
5.00
5.27
5.00

11.2
1.9
2.0
2.3
2.3

TC

maxKb/Kg
2271
4.8
1.2
1293
4.4
1.3
maxKb/Kg
181
111
0.6
0.8
1.0
1.0

Yutaka Nakamura, Jun Saita and Tsutomu Sato6quencies for each component and position. According to this table,comparing simultaneous and individual measurements, they arealmost equal for each other on natural frequencies, but there is large
difference for 1st mode shape. On the other hand, from H/V spectral
ratio, estimated natural frequencies are little lower but amplification
factor is close to the results estimated by simultaneous measurement.
The following explains the results of these analyzes in detail.
3.1.1. Simultaneous Measurements
Figure 3 shows the amplification spectra of the sites along the column
elevation against the site TC7, 26 steps from the lowest level in apedestal as a rigid block, as a result of the simultaneous measurement. It
is possible to draw the vibration mode for the entire frequency mode
because the phase can be grasped by the simultaneous measurement.
Please find an animation to visualize the vibration mode sweeping100

EW component

Amplification Factor (Reference Point TC7)

10

1

185
157
129
101
73
59
45
31
26

0.1
0.1

1

10

100

NS component
10

1

100
185
157
129
101
73
59
45
31
26

0.1
0.1

1

10

100

UD component
10

1

100
185
157
129
101
73
59
45
31
26

0.1
0.1

1

10

100

Frequency in Hz

Figure 3. Amplification Spectra of TC estimated from Simultaneous Measurements

Dynamic Characteristics of Memorial Columns

7frequency in website ([6]).
Figure 4 shows the vibration modes for each peak frequency withconsidering phase difference. These figures show that the number ofpeaks of EW component is larger than that of NS component, that thefirst peak frequency is 1.59Hz for both EW and NS components, and thatthe shape of the mode diagram is slightly differ from each other.
200
180

Step Numbers

160

Trajan's
ColumnMode Shape

140
120
100

3rd

80

19.165Hz_EW
8.984 Hz_EW
1.587 Hz_EW
20.288Hz_NS
8.984 Hz_NS
1.587 Hz_NS

2nd
1st
3rd.

60
40

2nd
1st.

20
0
-10

-5

0

5

10

15

Amplification Factor

20

25

Figure 4. Mode Shape of TC estimated from Simultaneous Measurement

The shape of mode diagram for the first peak frequency is smooth.
That of both EW and NS components seems to consist of mostly
bending deformation and only that of NS component is recognizedoverlapped slightly shear deformation.
Second order frequencies with large peak are estimated 8.99Hz foreach direction with the second order mode shape. Natural frequenciesof third order are estimated 19.17 Hz for EW and 20.29Hz for NS
with third order mode shape. There are many spectral peaks in response spectra. These peaks might be corresponding to the local damage of column.
For the bending vibration of a uniform cantilever, the natural frequency’s ratio between first order mode and second or higher mode isapproximately 1: 6.2669∙∙∙: 17.5449∙∙∙: ∙∙∙. In case of shear or torsional

Yutaka Nakamura, Jun Saita and Tsutomu Sato8

vibration, this ratio becomes 1: 3: 5: ∙∙∙. According to the result of microtremor measurement, it could be clearly recognized up to the natural frequency of third order mode, and the ratio is approximately
1:5.65:12.06 for EW component and approximately 1:5.65:12.76 for
NS component. Consequently the horizontal vibration of TC is estimated consisting of almost bending vibration.
According to the measurements on the terrace, there is torsional vibration at the frequency range between 14Hz and 19Hz, and reaching
maximum at 15.5Hz. At other frequency range torsional vibration can
not be recognized. At the range between 14Hz and 19Hz, the peak andthe trough of the vibration modes are interchanged intricately at eachmeasuring points on the column body, and this phenomena may appear the effect of torsional vibration (see an animation on website of
SDR, reference [6]). Shear wave velocity of TC is estimated 1900 m/s
from the predominant frequency of torsional vibration.
In addition, the vertical vibration of TC predominates at 25.6Hz,
and the vibration mode shape shows the first order. And the propaga200
180

Trajan's Column
Kb Distribution
by Simul. H/H

Step Numbers

160
140
120
100

3rd

80

2nd
1st.

19.165Hz_EW
8.984 Hz_EW
1.587 Hz_EW
20.288 Hz_NS
8.984 Hz_NS
1.587 Hz_NS

60

80

2nd
1st
3rd.

60
40
20
0
0

20

40

Kb (m/Gal)

100

Figure 5. Kb-value of TC estimated from Simultaneous Measurement

Dynamic Characteristics of Memorial Columns

9tion velocity of the longitudinal vibration of TC is estimated 3100 m/s,
and the Poisson's ratio is estimated 0.33 from the shear wave velocity
and it is a reasonable estimation as marble. However, because the estimated velocities of TC are about 65% of the typical value of marble,
4800 m/s for longitudinal vibration or 2900 m/s for shear wave, TC
seems to be considerably deteriorated.
Figure 5 shows a destructive index Kb value derived from the estimated amplification mode of horizontal vibration. Please see the detail of Kb value on reference [4] as a name of KT. According to thisfigure, the influence of the first order vibration mode is very large, and
it is possible to ignore the higher modes. Distribution of Kb values by
the first order vibration grows higher toward to the top, and reaches
the maximum value of 83μ/Gal at the top. Strong motion of PGA 100
Gal will cause 1/120 of drift angle at the top of column near terrace.
The ability of shear deformation of TC which is made simply bystacking large marble blocks must be considered.
3.1.2. Individual Measurements(1) Individual Spectral Ratio
Here the response spectrum ratio against control point is consideredin case of using not simultaneous measurement record.
Figure 6 shows estimated mode shape for several orders using
spectral ratio to point TC7. According to this, predominant frequencies by third mode are almost equal to the results of simultaneous
measurement. On the mode shape, however, the amplification factor
becomes larger close to the terrace, although higher mode shape arealmost same. Temporal or special stationarity of the column may be
disturbed by the activities of other investigation teams on the terrace
or inside the column body.
It is expected that the response characteristics can be estimatedproperly from the spectrum ratio against control point under keeping
stationarity in case of not simultaneous measurement. However it isobvious that disturbance of stationarity causes disturbance for the estimation result. Because the column seems to be impacted constitutionally by the shaking to upper part, it is also necessary for response
spectrum estimation to reconfirm to take countermeasure as limitation

Yutaka Nakamura, Jun Saita and Tsutomu Sato

10

200
180

Step Numbers

160
140

Trajan's Column
1st Mode120
100

Indiv.
Indiv.
H/V
H/V
Simul.
Simul.
Indiv.
Indiv.
H/V
H/V
Simul.
Simul.

80
60
40
20

1.587Hz_EW
Hz_EW
1.587
1.514Hz_EW
Hz_EW
1.514
1.587Hz_EW
Hz_EW
1.587
1.587Hz_NS
1.587
Hz_NS
1.440Hz_NS
1.440
Hz_NS
1.587Hz_NS
1.587
Hz_NS

0
0

10

50

20

30
100

200

Step Numbers

Step Numbers

Trajan's Column
180
2nd Mode160

Step Numbers

Step Numbers

40 150

140
120

60
200

200
180
160
140

Trajan's Column
3rd Mode

120

100

100

80

80
60

Indiv.
Simul.

9.033 Hz_EW 60
8.984 Hz_EW
40
9.033 Hz_NS
8.984 Hz_NS 20

-10

-5

Indiv.
Simul.

50

Amplification Factor

Indiv.
Simul.

40
20

Indiv.
Simul.

19.043Hz_EW
19.165 Hz_EW
20.264 Hz_NS
20.288 Hz_NS

5

10

0

0
0

Amplification Factor

5

10

-10

-5

0

Amplification Factor

15

Figure 6. Comparison of the Shape of Modes of TC between Various Methodsof other activities during measurement or conducting simultaneous
measurement.
(2) H/V and its ratio
Here, as a trial to estimate reasonable response spectrum from individual measurement using H/V spectral ratio. Response of verticalcomponent is rather clear than that of horizontal component at highfrequency range. However at lower frequency range, the characteris-Dynamic Characteristics of Memorial Columns

11

tics of vertical motion on the base ground are similar to that of horizontal motion. This idea uses these characteristics. In case of ground,a peak appears at a frequency corresponding to the predominant frequency of the surface ground, and the peak value gives approximately
the amplification factor. Also in case of structures, it is necessary to
notice that the H/V spectrum ratio sometimes reflects the motion as
rocking vibration.
100

EW/UD

Amplification Factor

10

1

0.1

185
157
129
101
73
59
45
31
26

1.514
0.1

1

10

100

100

NS/UD
10

1

0.1

185
157
129
101
73
59
45
31
26

1.440
0.1

1

10

100

Frequency in Hz

Figure 7. H/V Spectral Ratio at the Sites of TC

Figure 7 shows overlapped H/V of each point at TC. According tothis figure, the predominant frequency of 1.5 Hz corresponds to thefirst order natural frequency of TC. The frequency of 5.59 Hz is recognized at all points, and it can be considered as the natural frequency
for surface ground with about twice as amplification factor.
Figure 6 also shows a mode shape corresponding to the principal
frequency around 1.5 Hz. According to this figure, the abnormal phenomena of enlargement of amplification factor near the terrace can be
avoid, and estimated amplification factors and mode shape are similar
to the results of simultaneous measurement mentioned above. In caseof individual measurement, it is expected that the amplification factor
and mode shape can be estimated roughly by calculating the H/V or
the ratio of H/V.

Yutaka Nakamura, Jun Saita and Tsutomu Sato12

3.2. Column of Marcus Aurelius
On AC each microtremor measurement was conducted individually.
Table 2 shows an analytical result of measurement.
2. Resultsof
of Microtremor
Microtremor Measurementsof AC
TableTable
2. Results
Measuements
for ACAC
Individual
F Hz
maxAF maxKb/Kg
EW
1st
1.29
64.0
936
2nd
6.59
15.2
17.9
3rd
15.02
12.4
2.3
NS
1st
1.22
53.3
957
2nd
6.98
19.4
15.9
3rd
15.14
20.9
3.0
Longitudinal
1st
18.80
57.7
1.0

Torsional
AC
EWNS
Ground: MC7
CMGW

1st
2nd
H/V
1st
1st
1st
1st

9.13
25.95
F Hz
1.25
1.22
1.22
1.37

maxAF maxKb/Kg
18.8
212
13.9
144
2.54
5.3
2.76
5.6

100

EW component

Amplification Factor (Reference Point MC7)

10

1

190
162
134
106
78
50
22
0
-14

0.1
0.1

1

10

100

100

NS component
10

1

190
162
134
106
78
50
22
0
-14

0.1
0.1

1

10

100

100

UD component
10

1

190
162
134
106
78
50
22
0
-14

0.1
0.1

1

10

Frequency in Hz

Figure 8. Amplification Spectra of AC estimated from
Individual Measurement100Dynamic Characteristics of Memorial Columns

13(1) Individual Spectral Ratio
Figure 8 shows the individual spectral ratios of each point to point
MC7 corresponding to ground surface level. Figure 9 shows the modeshapes of first to third order vibrations. According to this figure, large
amplification is observed near the terrace for first order mode same asthat of TC, and it seems to reflect the activity of people. The influence
for higher mode may be smaller than the result of TC. Anyway, it isnecessary for grasping the exact response to conduct measurement at
another time. The natural frequencies of longitudinal and torsional
vibrations are estimated 18.8 Hz and 9.1 Hz, respectively. From thisthe propagation velocities are estimated 2300 m/s and 1100 m/s, respectively. The estimated velocity of longitudinal vibration is morethan 50 % lower than typical value, 4800 m/s. The shear velocity is also estimated too low to calculate the Poisson’s ratio. This is caused by
the low frequency of torsional vibration. As seen in Photo 1, there istrace of restoration for vertical damage clearly appears on west side ofAC, and this is considered as a reason why the frequency of torsional
vibration is very low.
200
180

Step Numbers

160
140

100
80
60
40
20

-20

3rd
2nd
1st
3rd.
2nd
1st.

120

0
-10
0
-20

15.015 Hz_EW
6.592 Hz_EW
1.294 Hz_EW
15.137 Hz_NS
6.982 Hz_NS
1.221 Hz_NS

Marcus Aurelius's
Column Mode Shape by
Indiv.H/H
10

20

30

40

50

60

70

Amplification Factor

Figure 9. Mode Shape of AC estimated by Individual Measurements

14

Yutaka Nakamura, Jun Saita and Tsutomu Sato

Metal Fasteners?

Photo 1. Damage of AC at West Side(2) H/V Spectral Ratio and etc.
Figure 10 shows overlapped H/V spectral ratio of each measurement point. The first order vibration mode shape is considered to similar to the result of the estimation from the H/V based on the discussion
for TC. Figure 11 shows the mode shapes of first order vibrations.

Dynamic Characteristics of Memorial Columns

15

100

190
162
134
106
78
50
22
0
-14

EW/UD

Amplification Factor

10

1

0.1
0.1

1

10

100

100

190
162
134
106
78
50
22
0
-14

NS/UD
10

1

0.1
0.1

1

10

100

Frequency in Hz

Figure 10. H/V Spectral Ratio at the sites of AC
200

Step Numbers

150

MarcusAurelius's Column
1st Mode100

Indiv.
H/V
Indiv.
H/V

50

1.294Hz_EW
1.245 Hz_EW
1.221 Hz_NS
1.221 Hz_NS

0
0

10

20

30

40

50

60

70

Amplification Factor-50

Figure 11. Comparison between First Mode Shapes of H/V and H/H of AC
from Individual Measurements

The destructive index Kb of AC is calculated from the estimation
result of amplification characteristics from H/V ratio, and Kb is compared with the result from the simultaneous measurement of TC. Figure 12 shows the results of comparison of Kb of TC and AC. Kb

Yutaka Nakamura, Jun Saita and Tsutomu Sato

16

200
180

Step Numbers

160

Kb Distribution ofTrajan's (simul.) andMarcus Aurelius's(H/V) Columns

140
120
100
80
60
40
20

H/V
Simul.
H/V
Simul

1.245 Hz_EW
1.587 Hz_EW
1.221 Hz_NS
1.587 Hz_NS

150

200

0
0

50

100

Kb (m/Gal)

250

Figure 12. Comparison between Estimated Kb-values for
TC (Blue mark) and AC (Green mark)value of TC grows lager towards to higher point reaching maximum
83 m/Gal. Kb values of AC shows variation at each point, and the
maximum value is 212 m/Gal near the terrace. In other words, drift angle over 1/120 will occur at TC with over 100Gal of seismic acceleration, and in case of AC the same level of drift angle will occur evenunder 50Gal. These columns are constructed only stacking the large
marble blocks with getting stability only by dead load. It is necessary
to consider losing the stability of columns by growing the rocking vibration caused by column-soil interaction.

4. Concluding Remarks
This paper describes the results of microtremor measurement for two
memorial columns, Trajan’s Column and Marcus Aurelius’ Column.
Natural frequencies of horizontal vibration are about 1.6 Hz for TC
and about 1.3 Hz for AC, and both of them seems to be caused bybending vibration. These are almost similar to previous researches.

Dynamic Characteristics of Memorial Columns

17

The natural frequencies of longitudinal and torsional vibrations ofTC are 25.6 Hz and 15.5 Hz, respectively. From this the propagation
velocities of the longitudinal vibration and the shear wave are estimated 3100 m/s and 1900 m/s, respectively. These velocities are low value, 65 % of typical value, but the Poisson’s ratio is reasonable, 0.33.
On the other hand, the natural frequencies of longitudinal and torsional vibration of AC are 18.8 Hz and 9.1 Hz, respectively, and from thisthe propagation velocities are estimated 2300 m/s and 1100 m/s, andthese are very low values. The velocity of longitudinal vibration of AC
is extremely low, under 50% of typical value. And the Poisson’s ratio
could not be calculated because of too slow shear wave velocity. The
natural frequency of torsional vibration of AC is extremely low reflecting
the longitudinal damage.
For the estimation of vibration mode, the results of simultaneous andindividual measurement were compared. Because the memorial columns
vibrate easily, it is confirmed that the result of measurement is easily
affected by the human activity inside the column and the affection isdifficult to avoid without simultaneous measurement. And also it isconfirmed that affection can be avoid with extended usage of H/Vspectrum ratio.
According to the results of calculating the destructive index Kb of
the columns that are based on the fundamental mode of bending vibration, Kb of TC grows larger toward to the top reaching a maximum of
about 83μ/Gal near the terrace, and that of AC shows variation at eachpoint and the maximum is 212μ/Gal near the terrace. In other words,
drift angle over 1/120 will occur over 100Gal of seismic acceleration
for TC, and in case of AC the same level of drift angle will occur evenunder 50Gal. Because both the columns are built with only stacking of
marble block, the columns ensure its behavior of the elastic body onlywith pre-stress caused by its own weight.
Therefore, if the effect of rocking vibration due to the coupling effect between columns and ground becomes large, it is easy to become
unstable. It seems that it will be important to conduct a detailed investigation and determine the limit of the ground motion.
By the additional detailed investigation based on the knowledge
obtained by this survey and by the sequential investigation with standardized research method, it is expected that the investigation will con-

18

Yutaka Nakamura, Jun Saita and Tsutomu Sato

tribute to the reasonable maintenance or restoration plan with grasping
the degree or location of damage quantitatively.
This time, simultaneous measurement was conducted only for TC. It is
desirable to measure TC and AC again completely for confirmation.

Acknowledgments
The measurement of memorial Columns in Rome was conductedunder the supporting of Professor Valente and Associate Professor
Tallini of L’Aquila University. We would like to express our thanks
for their helps.

References[1] Clemente, P. and et al.: La Colonna Antonina in Roma: Valutazione Dgli Esetti Delle Vibrazioni Ambientali, ASS. I. R. C. CO., 1988,
pp.207-217.
[2] Boschi, E. and et al.: Resonance of Subsurface Sediments; an
Unforeseen Complication for Designers of Roman Columns, Short
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