DYNAMIC CHARACTERIZATION OF TRAJAN'S COLUMN · 2014-07-09 · Dynamic Characterization of the Trajan’s Column 5 Figure 2: Sensors layouts a (left) and b (right) Time and frequency

SAHC2014 – 9th International Conference on

Structural Analysis of Historical Constructions

F. Peña & M. Chávez (eds.) Mexico City, Mexico, 14–17 October 2014

DYNAMIC CHARACTERIZATION OF TRAJAN'S COLUMN

P. Clemente1, G. Bongiovanni

2, G. Buffarini

3 and F. Saitta

4

1 ENEA, Casaccia Research Centre

Via Anguillarese 301, 00123 Rome, Italy

[email protected]



[email protected]



[email protected]



[email protected]

Keywords: experimental dynamic analysis, operational modal analysis, cultural heritage.

Abstract. The importance of studying the health status of monuments relies in their preserva-

tion effort but also in the historical analysis of earthquakes. The historical seismicity has been

reconstructed thanks to historical documents that reports descriptions about the damages of

monuments. This information is very important also because lots of monuments can still be

observed and analyzed and so the characteristics of past earthquakes can be estimated. But

the analysis and interpretation of the historical documents should also accounting for the

present structural health status of monuments, which is influenced by material degradation,

changes in loads, seismic actions, traffic-induced vibrations, presence of other buildings. The

experimental analysis plays and important role. The Trajan's Column in Rome has been the

subject of the study shown in this paper. Ambient and traffic-induced vibrations were record-

ed in order to characterize dynamically the column and to point out same aspects of its be-

haviour. The results have been compared with those obtained in previous campaigns.

mailto:[email protected]

mailto:[email protected]

P. Clemente, G. Bongiovanni, G. Buffarini and F. Saitta

2

1 INTRODUCTION

The Trajan’s Column, conceived by architect Apollodoros of Damascus, is a commemora-

tive monument decorated with reliefs illustrating the two military campaigns of the Roman

emperor Trajan in Dacia (modern Romania) between 101 and 102, and between 105 and 106

A.D., respectively. It was erected in 113 A.D., and was the first of several such monuments. It

is also an invaluable source of information about the Roman Army and a lasting testimony to

the Roman love of monumental architecture constructed to celebrate military victories and

Roman leaders. The column is 29.78 m tall and is composed by 19 blocks of Italian white

marble. It stands on an 8-block base and is topped by a two-block pedestal. Originally a 4.8 m

bronze statue of emperor Trajan stood at the top, then it was replaced by the statue of St. Peter

in 1588 A.D. After the emperor’s death in 117 A.D. his ashes were buried within the founda-

tions of the column. Figure 1 shows the column and interesting cross sectional view of the

structure [1]. During cleaning operation between 1980 and 1985 Giuffrè noticed some minor

cracks, a couple of which could be attributed to earthquakes [2, 3].

Figure 1: View of the Trajan's Column and the Rondelet relief of the structure [3]

The interest in the structural analysis of the Trajan’s Column relies in the preservation ef-

fort of historical monuments with particular reference to this structural type but also in the

analysis of historical earthquakes. In fact, the historical seismicity has been reconstructed

thanks to historical documents that reports descriptions about the damages of monuments.

This information is very important also because lots of monuments can still be observed and

analyzed and so the characteristics of past earthquakes can be estimated [4]. On the other

hand the analysis and interpretation of the historical documents should also account for the

present structural health status of monuments, which is influenced by material degradation,

changes in loads, seismic actions, traffic-induced vibrations, presence of other buildings. A

Dynamic Characterization of the Trajan’s Column

3

complete study should include a reliable experimental analysis and a successive numerical

modelling [5, 6, 7]. The first step is described in this paper. Ambient and traffic-induced vi-

brations were recorded, which allowed to characterize the column and to point out same fea-

tures of its dynamic behaviour.

2 PREVIOUS EXPERIMENTAL TESTS

2.1 Experimental analysis

In the framework of a large project organized by ENEA in collaboration with the So-

printendenza Speciale per i Beni Archeologici (SSBA) of Rome and ISMES the effects of the

traffic-induced vibrations on several monuments in Rome were investigate [8, 9, 10, 11]. The

Trajan's Column was one of these. The experimental study was carried out in the 1985. Data

analyses were performed both in time and frequency domain [12].

Eighteen Teledyne-Geotech seismometers were used, six of them were deployed in vertical

direction and twelve in horizontal radial and tangential directions (Figure 2). The signals rec-

orded in analog form on magnetic tape, were then amplified and filtered, and finally sent to an

A/D converter and acquired with a sampling step of 0.005 sec. Five measurement series were

performed, lasting 90 minute each, at different times of the day. The portions of recordings

with highest energy content were extracted and analyzed.

The main results can be summarized as follows. The vibration amplitudes recorded on the

column were very low, with peak values of 0.10 mm/sec along the column, and of 0.05

mm/sec on the pedestal; the velocity module on the basement was 0.14 mm/sec. The spectral

analysis pointed out a resonance frequency at 1.60 Hz, associated to the first modal shape of

the structure; other significant peaks were in the range [5.5, 9.0] Hz.

Figure 2: View of the column with sensors deployment and experimental first modal shape (previous experi-

mental campaign).


4

2.2 Numerical modeling

The finite element models of the column was composed of beam elements, fully con-

strained one to the other, with geometrical characteristics equal to those of the stone blocks,

and material characterized by a weight density =27.00 kN/m3 and a Poisson's ratio =0.25.

The value of the Young's modulus of the blocks was chosen in order to optimize the corre-

spondence between the experimental and numerical results (E=20000 N/mm2). The pedestal

was divided in four beam elements. Since the signal analysis did not show the presence of

soil-structure interaction effects, the column was considered fixed at its base.

The dynamic analysis gave the frequencies reported in Table 1, which were very similar to

those of the obtained experimentally, as well as the first modal shape (Figure 3).

Table 1. Experimental and numerical frequencies.

Mode Exp. freq.

(Hz)

Num. freq.

(Hz)

1 1.60 1.7

2 - 9.0

The numerical model was used in the response spectrum analysis performed according to

the Italian code assuming the input parameters valid for low seismicity areas. The effects of

the first three modal shapes were superimposed. The results obtained demonstrated that the

values of the ratio between the shear force and the normal force were quite low and, in partic-

ular, much lower than the dynamic and the static friction coefficients of the marble. Further-

more the stresses caused by environmental vibrations and weak earthquakes were low.

So the limitations of the model proved to be inessential, the basic assumptions being al-

ways satisfied. Actually, the assumption of linearity is valid as long as the friction between

the blocks is not exceeded and no tensile stresses are present, namely the resultant of the loads

is not out of the core of inertia at each section. In the first case slippage would occur, resulting

in the loss of the geometry of the column. In the second one the effective section changes and

the resistant structure varies. This last difficulty could be overcome by introducing no tension

gap elements in the model, corresponding to the discontinuity of the soft elements.

3 NEW INSTRUMENTATION AND TESTS

In March 2012 a new large experimental campaign was carried out. The instrumentation

used consisted of nine Kinemetrics short period (1 Hz) seismometers SS-1 connected to 1

Kinemetrics K2 recorder, positioned in two layout (Figure 3). In the first (Layout a):

• three sensors (CH01, CH02 and CH03, respectively in y, vertical and x direction) were

at the base of the pedestal, at the lowest level of the staircase,

• three sensors (CH08 and CH10 in y direction, CH09 in x direction) were at the base of

the column, just above the top of the pedestal,

• three sensors (CH11 and CH13 in y direction, CH12 in x direction) were at the top of

the column.

In the second one (Layout b):

• three sensors (CH01, CH02 and CH03, respectively in y, vertical and x direction) were

at the base of the pedestal, at the lowest level of the staircase,

• three couple of sensors were at the base, at the mid and at the top of the column, respec-

tively.


5

Figure 2: Sensors layouts a (left) and b (right)

Time and frequency domain analysis

The peak values and the effective peak values ( [∫ ( )⁄

] ⁄

, t2 - t1=1.28

sec) were calculated, distinguishing the portion of the record during the day and that during

the night, in order to estimate the effects of ambient noise due to different sources. From the

results, reported in Table 2, one can deduce that there is no evidence of significant variation

from day to night.

Table 2. Comparison of peak values in Layout a

Sensor Day peak

values

(mm/sec)

Day effective

peak values

(mm/sec)

Night peak

values

(mm/sec)

Night effective

peak values

(mm/sec)

13 0.0744 0.0366 0.0649 0.0262

11 0.0980 0.0419 0.0947 0.0316

10 0.1035 0.0361 0.1012 0.0395

08 0.1040 0.0370 0.0998 0.0408

01 0.0475 0.0170 0.0384 0.0177

12 0.1086 0.0490 0.0915 0.0338

09 0.0809 0.0291 0.0793 0.0336

03 0.0442 0.0148 0.0520 0.0193

02 0.0465 0.0196 0.0453 0.0212


6

All the tests have been analyzed in frequency domain by means of cross spectral analysis.

In figure 4 the power spectral densities (PSDs) of all the recorded signals are plotted. It is ap-

parent that:

• the motion of the column is dominated by two frequencies, equal to 1.45 and 1.51 Hz,

respectively,

• there are amplifications between 5.5-6.0 Hz, at about 6.5 Hz, 8.0 Hz and between 15.5

and 16 Hz,

• the cross analysis confirmed the structural resonance frequencies 1.45 Hz and 1.51 Hz,

which are associated to modal shapes of the whole structure, column and basement. In

figure 5 the cross spectra of the corresponding signals at the base and at the top of the

column are shown, along with phase relationships.

Figure 4: PSDs of the recorded signals

(a) (b)

Figure 5: Cross spectra (amplitude = continuous line, phase factor = dotted line) of signals in (a) x direction and

(b) y direction

Other minor translational frequencies, equal to 5.6, 5.8, 6.5 and 8.0 Hz respectively, were

evaluated for the whole structure. The cross analysis between the parallel sensors CH11 and

CH13 at the top shows that they are 180 degrees out of phase at 15.8 Hz (Figure 6). This

could be due to a torsional movement of the upper portion of the column but cannot be

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 2 4 6 8 10 12 14 16 18

PSD

((m

m/s

)^2

/Hz)

f (Hz)

az002 CH01

CH02

CH03

CH10

CH09

CH13

CH08

CH11

CH12

-180

-90

0

90

180

0.E+00

1.E-03

2.E-03

1.0 1.2 1.4 1.6 1.8 2.0

Ph

ase

(°)

CSD

(mm

/s)^

2/H

z)

f (Hz)

az004 CH03-CH12

-180

-90

0

90

180

0.E+00

1.E-03

2.E-03

1.0 1.2 1.4 1.6 1.8 2.0

Ph

ase

(°)

CSD

(mm

/s)^

2/H

z)

f (Hz)

az004 CH01-CH11


7

associated to an elastic torsional modal shape. The cross analysis of CH08 and CH10 showed

different features at this frequency, with non significant values of phase factor and coherence

function.

Figure 6: Cross spectrum (amplitude = continuous line, phase factor = dotted line) of signals CH11 and CH13

The translational modal shapes are plotted in Figure 7. The relevant amplification at the

top implies that non elastic rotations could interest the column also along its height.

Figure 7: Normalized modal shapes (black x direction)

Motion of the top

Since the closeness of the two dominant frequencies can produce relevant effects on the

global behavior of the monument, further analysis were carried out. The two orthogonal

signals CH12 and CH11 were first composed in order to have the component along any

direction defined by the angle with the x axis (from 0° to 180°). In figure 8 the spectrum of

this component along varying direction is plotted in the frequency range of interest (between

1.0 and 2 Hz). It is apparent that the main directions of the structure are non coincident with

the geometrical ones of the pedestal.

The velocity time histories at the top of the column of signals CH12 and CH11 were fil-

tered between 1.3 and 1.8 Hz and then integrated to get the corresponding displacement. The

-180

-90

0

90

180

0.E+00

5.E-06

1.E-05

14.0 15.0 16.0 17.0 18.0

Ph

ase

(°)

CSD

(mm

/s)^

2/H

z)

f (Hz)

ax004 CH11-CH13

0

10

20

30

40

-1 -0.5 0 0.5 1

az002

1.45 x

1.51 y

5.60 y

5.80 x

6.50 y

8.00 x

8.00 y


8

particle motion is shown in figure 9a for a time interval of about 10 sec. The motion of the

column consists in an oscillation around an axis varying in time. Figure 9b shows the distribu-

tion of the angular position of the particle for angle interval of 5°. It is apparent that there are

preferred directions.

Figure 8: Spectrum of the component along varying direction

(a) (b)

Figure 9: (a) Particle motion at the top of the column and (b) distribution of the angular position

Angle and modulus of the particle motion showed the periodicity illustrated in figure 10.

The power spectral density of the angle function has a first peak at the same resonance fre-

quencies of the column (1.45 and 1.51 Hz) and the others at frequencies multiple of these. The

PSD of the modulus presents peaks at frequencies double of those of the column and the oth-

ers at frequencies multiple of these.

Other feature of the motion associated to the two main frequencies are the following. The

difference between CH13 and CH11 (y direction), presents a periodicity close to 1.46 Hz,

which is the resonance frequency of the mode with prevalent displacement in x direction.

Conversely, the difference between CH08 and CH10 (y direction, at the base of the column)

presents a periodicity of 1.51 Hz (Figure 11).


9

(a) (b)

Figure 10: PSD of (a) angle and (b) modulus of particle motion

(a) (b)

Figure 11: Spectra of differential motion (a) at the top and (b) at the base column

4 CONCLUSIONS

The monument appears like a quite simple structure with axial symmetry both of the ped-

estal and the column, but it is not. Previous results, obtained with older instruments and data

analysis methods, showed only one translational mode at 1.6 Hz, while the recent study point-

ed out:

• two dominating translational frequencies very close each to the other, 1.46 and 1.51 Hz;

as a result the column oscillates around a varying axis, although preferred direction of

the motion are apparent;

• four translational frequency, at 5.6, 5.8, 6.5 and 8 Hz respectively, are present;

• a torsional motion of the top of the column at 15.8 Hz, which cannot associated to an

elastic modal shape.

So far, even for very low level of excitation, the structure exhibits unexpected features.

The reasons of these should be searched in the following:

• non homogeneous mass distribution, due to the presence of the spiral staircase but also

to restorations;

• non homogeneous mechanical properties of the marble subject to degradation, related to

the exposition to weathering, earthquakes and ambient vibrations for about 2000 years;

• presence of links between blocks, both in vertical and horizontal directions, some of

which are visible, whose effectiveness should be analyzed;

• the static and dynamic soil-structure interaction [13].

All these uncertainties should be clarified in order to analyze properly the health status of

the monument and to evaluate its capability to support future dynamic actions, related to

earthquakes, wind, ambient or traffic-induced vibrations.

0

5

10

15

20

0 2 4 6

PSD

TET

A

f (Hz)

az002 (CH12+CH11)

0.E+00

2.E-05

4.E-05

6.E-05

0 2 4 6

PSD

MO

DU

LUS

f (Hz)

az002 (CH12+CH11)

0.E+00

2.E-07

4.E-07

6.E-07

1.2 1.4 1.6 1.8

PSD

(mm

^2

/HZ)

f (Hz)

CH13-CH11

0.E+00

5.E-09

1.E-08

1.2 1.4 1.6 1.8

PSD

(mm

^2

/HZ)

f (Hz)

CH08-CH10


10

5 ACKNOWLEDGMENTS

The Authors thank the Soprintendenza Speciale per i Beni Archeologici (SSBA) of Rome

for allowing this study and are particularly grateful to Cinzia Conti, the responsible for the

Trajan's Column.

6 REFERENCES

[1] Giuffrè A.. Valutazione della vulnerabilità sismica dei monumenti: metodi di verifica e

tecniche di intervento. La colonna Antonina. Studi e ricerche sulla sicurezza sismica dei

monumenti, Report No. 6, 1984.

[2] Giuffrè A., Ortolani F.. Le colonne coclidi testimoni dei terremoti di Roma. Studi e ri-

cerche sulla sicurezza sismica dei monumenti. Sapienza Università di Roma, Report No.

7, 1988.

[3] Rondelet J. B.. Trattato teorico e pratico sull’arte di edificare (Italian translation from

French, http://risorseelettroniche.biblio.polimi.it/rondelet, 1831.

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19, 107-118.

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Obelisk. Proc. 14th

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la Minerva Medica. Proc. 10th European Conf on Earth Eng., Vienna, 28 Aug.-2 Sept.,

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[11] Clemente P.. Traffic-Induced Vibrations on Structures. IABSE Report Extending the

Lifespan of Structures, 73(2), 1111-1116, 1995.

[12] Clemente P.. Vibrazioni indotte dal traffico: un’insidia per i monumenti. In Complessità

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[13] Boschi E., Caserta A., Conti C., Di Bona M., Funiciello R., Malagnini L. , Marra F.,

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http://risorseelettroniche.biblio.polimi.it/rondelet

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DYNAMIC CHARACTERIZATION OF TRAJAN'S COLUMN · 2014-07-09 · Dynamic Characterization of the Trajan’s Column 5 Figure 2: Sensors layouts a (left) and b (right) Time and frequency