Prepared for 12th WCEE 2000 in Auckland, NZ
2660/6/A

VULNERABILITY INVESTIGATION OF ROMAN COLOSSEUM USINGMICROTREMOR

Yutaka NAKAMURA1, E.Dilek GURLER2, Jun SAITA 3, Antonio ROVELLI4, Stefano DONATI5
SUMMERY
Preservation of monuments all around the world and increasing their stability against earthquakes is an
important issue for many countries. For this purpose, there are many efforts for reinforcing or repairing
the monuments, as well as accurate damage estimation for the future earthquakes. Among the otherwonder of the world, with its huge size and ring shape Roman Colosseum is the most imposing
monuments in Italy. It was built on the area that was previously occupied by the artificial lake andseveral times it has been destroyed by the earthquakes. The purpose of this study is to investigate thedynamic characteristics of Colosseum and identify the main damage mechanism to evaluate the risk ofdamage or collapse of various points of the structure. Among the other approaches, microtremor is theeasiest and cheapest way to understand the characteristic features without causing any damage to thestructure. Detailed measurements were performed at each floor and vulnerability indices called K-values
which are simply derived from strains of ground and structure, proposed by Nakamura (1996, 1997) arecalculated and weak points that may collapse during the earthquake are found. This analysis resulted thatdynamic characteristics of Colosseum consists of two parts that can be named as inner and outer walls.
From the preliminary analysis, predominant frequency and amplification factor for outer part are foundas 1.5 Hz and 3, respectively. And the inner part has a value of 3Hz for the predominant frequency and7-10 for amplification factor. Different mode shapes of the structure are also simulated. Relating withcalculated K-values, maximum acceleration value that different points in Colosseum can accept is also
calculated and proposed as a new index of earthquake resistance. The reliability of this new index ischecked by relating with the damage on outer structure caused by 1349 Appennino Central Earthquake.
INTRODUCTION
It is well known that, degree of damage during earthquakes strongly depends on dynamic characteristics ofbuildings as well as amplification of seismic waves. Because of this, behaviors before reinforcing or repairingthem should be investigated in advance. The Colosseum, known also as the Flavian Amphitheatre (Figure 1),
was built by the flavians in the middle of the broad valley, where Nero had sited the lake in the gardens of his
Domus Aurea. It was the most imposing of all the monuments in the ancient Rome. According to the Italianearthquake catalog, there are several earthquakes (508, 801, 1349, 1703) caused huge damage in the city ofRome and affected the Colosseum (Funicello et.al., 1995; Mozco et. al, 1995). The purpose of the present
study is to investigate the vulnerability characteristics of Roman Colosseum with a new technique that uses
microtremor. Since, monumental structures are not suitable for laboratory experimentation and all works
should be carried out directly on the buildings, in the present study microtremors are used for this purpose.
Italy is seismically very active and has number of monuments that are affected by the earthquakes. With
spectral analysis of microtremor records, predominant frequencies, amplification factors, vulnerable points
and modal shapes could be determined. Information about Colosseum together with the brief formulation of
the applied technique and results from the analysis are given in following sections.
1

System and Data Research Co., Ltd., 3-25-3 Fujimidai, Kunitachi-shi, Tokyo,Japan . E-mail:
System and Data Research Co., Ltd., 3-25-3 Fujimidai, Kunitachi-shi, Tokyo,Japan
3
System and Data Research Co., Ltd., 3-25-3 Fujimidai, Kunitachi-shi, Tokyo,Japan2

4
5

Istituto Nazionale Di Geifisica, Rome, ITALY
Istituto Nazionale Di Geifisica, Rome, ITALY

yutaka@sdr.co.jp

INFORMATION ABOUT COLOSSEUM
From AD 75 to AD 80, Colosseum’s construction took just 5 years to complete. It can be considered as anarchitectural wonder especially with its extraordinary dimension. It has an elliptical plan with a circumferenceof 537m, the major axis of its ellipse is 188m long, the minor axis attains 156m, and the walls in the outer ringrise to almost 50m above ground. Cross section is given in Figure 2.

Figure 2: NS cross-section across the central
axis of Colosseum.

Figure 1: Aerial view of Colosseum.
According to the historical documents, Colosseum’s construction required 100000 cubic meters oftravertine, 6000 tons of concrete and metal cramps that more than 300 tons. To ensure the maximum
possible speed of construction, the site was divided into four sectors and these sectors were further
organized according to the materials and the height required, in accordance with a detailed plan, for
optimizing costs. It consists of 80 radial walls, converging from the outer to the inner ring, which supported
the great auditorium made of travertine blocks, and the complex system of tunnels and staircases. Theinterior of the Colosseum consisted of the arena, a wooden floor sustaining a bed of sand and covering an
area of about 76m by 46m, below the arena a complex system of passages and rooms extended. The
load-bearing structure is made of carved stone blocks, and the vaults between one and the next were cast in
concrete. The blocks were not held together with mortar but with pins of iron and other metals. The outer
perimeter ring consists of four stories: the first three each had 80 arches which supported one another.
According to the historical sources the Colosseum suffered several types of damage related to earthquakes(Funicello et. al, 1995; Mozco et.al, 1995). In particular, the damage is mostly concentrated in the southern
portion of the amphitheater where geological features shows a Holocene alluvial valley which shows poor
geotechnical characteristics including significant amplification of ground motion. The effect of the local
geological structure underlying the structure on seismic ground motion is investigated by Mozco et.al,(1995). Northern part of the Colosseum is underlain by an almost horizontal layer of Pleistocene continental
deposits. Figure 3. shows local geological conditions in and around the amphitheater. The soft river deposits
create a well confined and relatively deep sediment filled valley which may cause al large variability of theseismic ground motion within the Colosseum area. And Funicello et. al.(1995) also mentioned that, there isa coincidence between the trend of valley and southern portion of monument where nearly all the damage isconcentrated during the past earthquakes.
OUTLINE OF MEASUREMENT AND ANALYSIS
Measurement: An instrument named Portable Intelligent Collector (PIC) was used for microtremor
measurements. PIC includes two sensors, connection cables, main body installed in a metal case that
contains A/D converter, portable computer and amplifiers. Three components (two horizontal and one
vertical) of microtremor are recorded at every measurement points. Sampling interval is 1/100 sec and thelength of each record is 40.96 sec. Measurement was repeated three times at each observation point.
Figure 4 shows the location of measurements at ground, 1st, 2nd, 3rd,4th floors. And figure 5. shows some2views from the measurement area.

Figure 3: The geological conditions and sketch of cross section together with ground conditions(from Funicello et. al., 1995).
Analysis: After measurements, Fourier spectrum for each components are calculated and smoothed eighty
times with Hanning spectral window. With this operation band width approximately becomes 0.5Hz. One
frequency spectrum of one component was estimated by averaging the three Fourier spectra. Vibration
mode characteristics are also investigated from spectral ratio of higher floors with ground floor.

Figure 4: Location of measurements at ground, 1st, 2nd, 3rd,4th floors are shown with ☆,{,◆,g,▲,respectively. Spectrums shows the QTS results of basement floor measurements.
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a)
b)
c)
d)
Figure 5: Views from measurement area, View from a) basement, b) 2nd floor c) 4th floor,d) Measurement at second floor.
Deformation of Structures During Earthquakes and Vulnerability Index (K values) for Structures:
Deformation of structures are related with seismic motion of the basement, dynamic characteristics ofsurface layer and structures. And to estimate possible damage for the future earthquakes, it is important toknow the present durability condition of the ground and structure correctly. For this vulnerable weak pointsof the structures should be investigated in advance. Figure (6) simply shows the mode shape anddeformation characteristics of nth floor structure.
Horizontal displacement δj shown in Figure 5.can be written as in equation (1),

δj =

α sj

(1)

(2πFs )2

Fs is a predominant frequency of structure. Story drift angle for jth story γj is expressed as follows,γj=δ j − δ j −1hj=

α sj − α sj −1(2)

4π 2 Fs h j
2

α sj = Asj ⋅ α g= Asj ⋅ A g ⋅ α b(3)= Asgj ⋅ α bHere, Ag and Asj are an amplification factor for ground and jth floor of the structure, respectively. Asj isderived from Sjh and Sgh which are horizontal spectrum of jth floor and ground floor respectively. And Asgj isderived from the ratio of Sj and vertical spectrum of ground floor and represents combined amplification
factor of surface ground and structure. αb and αg are horizontal acceleration of basement and ground surface,respectively.

αsn

Wn

n

δn

hn

αg

αsj

Wj

j
hj

αs1

W1

1
h1

δj
δ1

Figure 6: Derivation of mode shapes of nth floor
structures. δj is the horizontal displacement, W is
the weight of the jth floor, hj is the height of jth
column, αb , αg , αsj are the horizontal accelerationof the basement, ground surface and jth floor of
the structure, respectively.

αb4

If unit of drift angle γj is 10-6, hj is meter and seismic acceleration is measured in unit Gal (cm/sec2), thanwith the unit adjustment, equation (2) can be written in following form,

γ j = 10 4 ⋅(A − A )sgj −1sgj

4π F ⋅ h j
2

2

⋅α b

(4)

From equation (4) KTgj value (representing vulnerability index for ground and building) is defined as,(

K Tgj = 10 4 (Asgj − Asgj −1 ) 4π 2 Fs ⋅ h j
2

)

(5)

unit of K values given above become 1/Gal. From this, vulnerability index for buildings can be written as,(

K Tj = 10 4 (Asj − Asj −1 ) 4π 2 Fs ⋅ h j
2

)

(6)

Maximum allowable acceleration from jth column αbaj ( in Gal) derived from equation (4) is,α saj = 10 ⋅4

4π 2 F 2 ⋅ h j
Asgj − Asgj −1⋅ γ aj(7)

Detail explanation and examples of the application of this technique can be found in Nakamura (1996,1997).
RESULTSQTS spectrums (Nakamura, 1989) at basement level are given in Figure 4 together with measurement point
locations. On west, south, east side of the basement, there is a peak around 1.2Hz with the amplification
factor of 1.5, but these peaks are not so reliable and especially on the north side is not so clear probably
because of the effect of the structure and traffic noise around this part. Effects of Rayleigh waves are clear
at all points.
From spectral ratios of each points, where measurements were done simultaneously, different peaks causedby different modes of the structure were found. Figure 7 shows the distribution of Amplification factor(A) for simultaneously measured points at ground and upper floor levels at 1.5 Hz frequency.
R Direction, F=1.5Hz

T Direction, F=1.5Hz
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1F A
1F F
2F A
2F F
3F A
3F F
4F A
4F F

4
3

Amplification Factor (A)Amplification Factor (A)

5

2
1
0

1F A
1F F
2F A
2F F
3F A
3F F
4F A
4F F

4
3
2
1
0

0

10

20

30

40

50

60

70

80

0

Measurement No.

10

20

30

40

50

60

70

80

Measurement No.

Figure 7: Distribution of amplification factor for R and T directions for F=1.5 Hz frequency.
As we can follow, there are no peaks for the points from 6 to 25 (location of these points are shown in
Figure 4). For both first and second floor levels, 1.5Hz peak with amplification factor about 4.5 in radial (R)and 3.5 in transversal (T) direction starts from the point 25 on the outer wall. This point is the one which isconnected with the supporting triangular wall. Peaks continue till point 60 which outer wall ends.
Amplification is high along the radial direction for many points of outer wall. This can be concluded as
1.5Hz vibration is caused by the effect of outer wall. Similarly Figure 8 shows distribution of A for about
3Hz. For the first floor, amplification factor having the value of 13 in radial component is high especiallyfor the beginning and the ending points of the outer wall which starts from 25 and continues till 60. There
are no strongly amplified points at upper floor levels for this frequency.
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Amplification in radial direction for the first floor is about three times bigger than the transversal direction
for point 25 and 60. This can be concluded as, structure is weak for the effects coming from the radial
direction. Although triangularly shaped supporting wall supports the system in transversal direction, thewall is weak to the motion at radial direction. Figure 9 shows that at 4.5Hz in radial direction, amplificationon the first floor level is high at points 15, 25 and especially at 70 having a value of 16. Amplification at thisfrequency for the upper floor levels is small.

T Direction, F=3.0Hz

R direction , F=3.0Hz
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1F A
1F F
2F A
2F F
3F A
3F F
4F A
4F F

12
10
8

Amplification Factor (A)Amplification Factor (A)

14

6
4
2

1F A
1F F
2F A
2F F
3F A
3F F
4F A
4F F

12
10

0

8
6
4
2
0

0

10

20

30

40

50

60

70

80

0

10

20

30

Measurement No.

40

50

60

70

80

Measurement No.

Figure 8: Distribution of amplification factor for R and T directions for F=3.0 Hz frequency.
T Direction, F=4.5Hz

R Direction, F=4.5Hz
16

1F A
1F F
3F A
2F F
3F A
4F F
4F A
4F F

14
12
10
8

Amplification Factor ( A)

Amplification Factor (A)

16

6
4
2

1F A
1F F
2F A
2F F
3F A
3F F
4F A
4F F

14
12
10
8
6
4
2

0

0

0

10

20

30

40

50

60

70

80

0

10

20

30

Measurement No.

40

50

60

70

80

Measurement No.

Figure 9: Distribution of amplification factor for R and T directions for F=4.5 Hz frequency.
Vulnerability index, KTj values are also calculated from the equation (6). Figure 10 shows the distribution of KT1
values on the first floor at inner wall through the whole ring, for 1.5Hz. This distribution shows the vulnerable
points. High K values at points 25, 30, 40, 55, 60 in figure 10, also shows that these points have higher risk ofdamage for inner wall. Figure 11 shows KT1 values again for the first floor but outer. In outer wall, having a valueof 110, K value is extremely high at point 25 showing the weakness of this point. Similarly figure 12 shows the
distribution of KT2 values for second floor for 1.5Hz. At this figure, points 26 and 59 have K value as 150 and 60
respectively, again showing the high risks at these points. KTj values are also calculated for 3.0 Hz. frequency andshown in figure 13, 14 and figure 15 for first and second and fourth floor levels, respectively. Similar with 1.5 Hz
frequency, figure 14 shows high values of K at points 25 and 59. In figure 15, K values are not high for second
floor, comparing with 1.5Hz frequency. And finally Figure 15 shows KT4 values for 3.0Hz. At this level, point 40
has higher risk than the other points.
60
R
T

40

KT1 Values

K T1 Values

KT1 values for 1st floor, F=1.5Hz
Outer wall120

KT1 values for 1st floor, F=1.5 Hz

20

R
T

80
40
0

0
0

10

20

30 40 50 60
Measurement No

70

0

80

Figure 10: KT1 values for 1st floor level, F=1.5Hz

10

20

30
40 50 60
Measurement No

70

80

Figure 11: KT1 values for 1st floor, F=1.5 Hz.
6KT2 values for 2nd floor, F=1.5Hz

KT1 values for 1st floor, F=3.0Hz
60
R
T

120

R
T

KT1 values

KT2 Values

160

40

80

20

40

0

0
0

10

20

30

40

50

60

70

0

80

10

20

Measurement No

30
40 50 60
Measurement No.

70

80

Figure 12: KT2 values for 2nd floor level, F=1.5 Hz Figure 13: KT1 values for 1st floor level, F=3.0Hz.
KT4 values for 4th floor

KT2 values for 2nd floor, F=3.0Hz
60

R
T

40

KT4 values

KT2 values

60

20
0
0

10

20

30 40 50 60
Measurement No.

70

R
T

40
20
0

80

0

10

20

30

40

50

60

70

80

Measurement No.

Figure 14: KT2 values for 2nd floor, F=3.0Hz

Figure 15: KT4 values for 4th floor, F=3.0Hz.

Figure 16: Vibration mode for 1.5Hz from point 25 to point 55. R direction(left) and T direction(right).

Figure 17: Vibration mode for 3.0Hz, from point 25 to point 57. R direction(left) and T direction (right)
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Maximum acceptable accelerations for vulnerable points mentioned above are also calculated from equation (7).
Calculation was made for 1.5Hz and 3 Hz for the points where calculated K values are very high. These are 25
and 59 for both first and second floor levels. KT1 value for point 30 for 1.5 Hz is about 29 and γaj is taken as
1/200. Then from equation (7) maximum acceptable acceleration is about 172Gal for this point of outer wall. And
for3.0 Hz for the same point, KT1 is about 25 and maximum acceleration is calculated as 200Gal. These values
are checked with the conditions caused by 1349 earthquake. For 1349 earthquake the reported modified Mercalli
intensity is VIII which correspond to an acceleration of 175 Gal. The calculated maximum acceptableacceleration value is between this values and consistent with the damage in the outer wall during this earthquake.
Same calculation for point 60 gives 238Gal for 1.5 Hz and 151Gal for 3.0Hz. KT2 values at second floor level forpoint 25 and 59 are 142 and 59 respectively for radial direction. Maximum accelerations at these points for 1.5Hz
are 35Gal and 85 Gal, and for 3.0Hz 119Gal and 147Gal, respectively. These values show that, MM VI-VII
earthquake which correspond to acceleration about 67Gal will be enough to cause more damage in vulnerable
points of Colosseum.
CONCLUSIONS
A method for investigating the vulnerability of structures is introduced. Using microtremor data, in a shortperiod of time, present method is able to give valuable information about the natural frequency, amplification
factor, vibration mode characteristics as well as week points of every type of ground and structures. With thepresent approach by defining weak points, it is possible to obtain real earthquake damage before earthquake
occurs. Analysis of Colosseum with this approach gave results as follows: Predominant frequency andamplification factor for the ground are 1.2Hz and 1.5, respectively, but these peaks are not so reliable andespecially on the north side is not so clear probably because of the effect of the structure and traffic noise aroundthis side. Dynamic characteristics of Colosseum interpreted as consisting of two parts named as inner and outerwalls. The predominant frequency and amplification factor for outer wall are 1.5Hz and 3, respectively. And
3.0Hz and changing between 7 and 10 for amplification factor for inner wall. Maximum acceleration values
calculated for vulnerable points that are grasped by K values checked with the acceleration value caused by 1349
earthquake. It successfully explains the damage of outer wall during this earthquake. As well as historicalmonuments, present approach also gives possibility for detecting changes in dynamic properties, which can be asignal of damage or weakness of the structure.
Maximum acceptable acceleration values for point 25 where the supporting wall has a connection showed that,
this point is very weak especially in the radial direction and may have more damage from MM VI-VII intensity
earthquake.
Making quick and precise damage estimation possible this type of preparatory study in highly seismic areas isvery promising for the future disaster prevention activities.
REFERENCES
Nakamura, Y., (1989),” A Method for Dynamic Characteristics Estimation of Subsurface using Microtremor on
the Ground Surface”, Quarterly Report of RTRI, Railway Technical Research Institute(RTRI), Vol. 30, No.1.
Nakamura, Y., (1996),” Real Time Information Systems for Seismic Hazards Mitigation UrEDAS, HERAS, PIC”,
Quarterly Report of RTRI, Vol. 37, No. 3.
Nakamura, Y., (1997), “Seismic Vulnerability Indices For Ground and Structures Using Microtremor”, World
Congress on Railway Research in Florence, Italy, November 1997.
Funicello, R., Lombardi, L., Marra, F., Paratto, M., (1995), “Seismic damage and geological heterogeneity inRome’s colosseum area: are they related?”, Annali di Geofisica, Vol. 38, Np.5-6, Nov-Dec, pp. 927-937.
Mozco, P., Rovelli, A., Labak, P., Malagnini, L., (1995), “Seismic Response of the Geological structure
underlying the Roman Colosseum and 2-D resonance of a sediment valley”, Annali di Geofisica, Vol. 38, Np.5-6,
Nov-Dec, pp. 939-956.

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