In Situ Traffic Vibration Monitoring and NonDestructive Analyses of the Egyptian Obelisk of San Giovanni in Laterano in Rome
Gerardo De Canio, Massimiliano Baldini, Stefano Bonifazi, Alessandro Colucci, Francesco Di Biagio, Marialuisa Mongelli, Angelo Tatì, Paola Giaquinto
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^{nd}; it was positioned at the current location in the XVI century by the architect Domenico Fontana. The obelisk stands on a 10m tall basement and, considering also the crux on the top, the total height of the monument is 45 meters. An extensive campaign of six months ambient vibration monitoring, sonic tomography and radar investigation has been carried out by ENEA for the structural evaluation of the obelisk
Introduction
The “Obelisco lateranense” is 32 m tall, and is composed by three blocks of granite connected to each other and at the base by three joints, the mechanical characteristics of which have been investigated and described in this article. The obelisk stands on a basement 10m tall and, considering also the crux on the top, the total high of the monument is 45 meters. Regarding its general structural conditions, once again it is possible to verify the high level of the Renaissance architectural skill while the three blocks are perfectly connected. The NonDestructive Analyses have highlighted the ingenious system of “crux joints” realized by the architect Gian Domenico Fontana to recompose the three blocks and the complex and useful dislocation of the blocks of granite at the base of the obelisk. The following in situ experimental campaign has been carried on for the structural evaluation of the obelisk :
 Structural monitoring and dynamic characterization by ambient vibrations;
 NonDestructive Analyses for the mechanical characterization of materials and identification of the metallic bars in the granite.
Structural Monitoring and Dynamic Characterization
The traffic close to the obelisk is regulated by 4 traffic lights, at each green light there is at least one heavy truck or bus. The trafficlight in via dell’Amba Aradam has a red light time of 40 sec and green light time of 80 sec. Therefore, to achieve the traffic lights vibrations, the time history data are 120 sec long. Figure 1 shows the frequency contribution to the RMS acceleration at different levels of the obelisk recorded on December 1^{st}, 2007, at time 16:37:53. In the graph, the signatures at 1.3 Hz and 6.1 Hz are evident, corresponding to the principal components of the Obelisk in the elastic phase. The figure also shows the time history and spectrogram of the induced acceleration when traffic light is green.
Fig. 1. Power Spectral density and Frequency contribution to the RMS acceleration value (in cm/sec^2). Spectrograms and time history during the green phase of the traffic light
Source: ENEA
Fig. 2. Accelerations due to the traffic from via dell’Amba Aradam to Piazza di porta S. Giovanni Source: ENEA
In terms of energy, traffic solicitations can be normalised with respect to a reference spectral acceleration, and evaluated comparing the spectral contents of the reference and the measured accelerations. In other words, a correspondence between the traffic effect and the reference earthquake of the site has been defined
Fig. 3. Confrontation between the maximum equivalent spectrum due to the traffic and the design earthquake spectrum of the site (OPCM 3431 the 2005may3th)
Source: ENEA
This way it is possible to evaluate the effects of the traffic vibrations in terms of normalised accelerations with respect to the reference earthquake. The curve MAX <Sa(T)_Traffic> is the envelope of the spectra at the base of the obelisk at 1.3 Hz and 6.1 Hz ( the principal modes of the obelisk). The ratio between traffic spectrum and site spectrum at the principal frequencies of the obelisk are shown in Table 1.
Table 1. Ratio between traffic and site spectrum at the principal frequencies of the obelisk
Mode No. 
Hz 
Sa(T)_traffic/ Sa(T)_site 
Sa(T)_traffic/ Sa(T)_OPCM 
1 
1.3 
0.013 % 
0.600 % 
2 
6.1 
0.040 % 
0.024 % 
Source: ENEA
The equivalent seismic action due to the traffic is 0.6% of the seismic demand for the Ultimate Limit State (Ref. OPCM 3431) and 0.04% of the site macro seismic spectrum.
With reference to the UNI9916 of 2004, the maximum ambient vibrations allowed for class 3 structures (monuments) is 0.25 cm/sec. Table 2 represents the ratio between these maximum values and the traffic equivalent velocity spectrum at the natural frequencies of the obelisk.
Table 2. Ratio between the maximum allowed ambient vibration and traffic equivalent velocity spectrum
Mode No. 
Frequency Hz 
Max<Sv(T)_Traffic> 
Ratio Max<Sv(T)_Traffic>/UNI9916 
1 
1.3 
0.0034 
1.36% 
2 
6.1 
0.00057 
0.22% 
Source: ENEA
Sonic and Radar NDT Investigation
The Obelisk is assembled by three blocks of granite jointed by hinges with unknown mechanical characteristics. Up to 4 zones have been identified to characterize the geometrical and mechanical behaviours of the obelisk, therefore both sonic and radar investigations have been performed to identify the geometry and characterize the mechanical properties. Knowing the differences between the mechanical characteristics of the representative zones of the obelisk it is possible to perform a parametric analysis of the dynamic response in terms of mechanical characteristics normalised with respect to the reference zone. Since the mechanical properties for the nondamaged zone are unknown, a parametric analysis have been performed and, for each parametric value, the properties for the other zones have been assessed according to the sonic and radar NDT experimental results. Figure 4 shows the sonic tomography results at different levels of the Obelisk. The sonic tomography allowed to verify the presence of iron staffs and bronze plates at the base of the Obelisk and also the presence of the joints with crux to avoid sliding between the three blocks.
Fig. 4. Sonic tomography at different levels of the obelisk
Source: ENEA
The radar investigation of the Obelisk has been performed in order to evaluate the characteristics of the joints. The following results were achieved:
 The base of the Obelisk has nonhomogeneous parallel blocks along the east, north and west sides.
 Inside each ring there are nonhomogeneous materials.
 Metallic plates and rods in symmetric positions 5050cm deep
Fig. 5. Radar echoes at the base of the Obelisk due to metallic bars and discontinuity between blocks
Source: ENEA
Numerical Analysis
The numerical analysis of the Obelisk has been performed assuming the properties of the materials as resulting by the NDT investigations and referenced to the parametric properties of the granite in good conditions. A parametric evaluation has been performed assuming different values of the elasticity modulus within the value range of 12 GPa and 45 GPa:
p_{granito}= 2700Kg/m^{3} ; ν=0.14 ; 1.25 E+10 < E [Pa] < 4.5E+10
A static non linear analysis has been performed considering the following distribution of the seismic action:
 typea seismic forces applied at the gravity center of the obelisk
 typeb seismic forces distributed at the gravity centers of the blocks
 typec seismic forces proportional to the first two modes
Fig. 6. Distribution of seismic loads for typeC forces: a) Seismic load C_I, b) Seismic Load C_II
Source: ENEA
Table 3 summarizes the results of the numerical analysis with different seismic load distribution.
Table 3. Critical acceleration multiplier evaluated assuming different seismic load
Seismic load: 
Critical multiplier 
a : Gravity + seismic action applied at the gravity center of the obelisk

11.25% 
b: Gravity + seismic action distributed at the gravity centers of the blocks 
12.0% 
cI : Gravity + seismic action proportional to the first mode of the obelisk 
12.5% 
cI : Gravity + seismic action proportional to the second mode of the obelisk 
15.0% 
Source: ENEA
Conclusions
The identification of the dynamic response of the Egyptian Obelisk of Piazza San Giovanni in Laterano in Rome, Italy, has been performed by means of longterm monitoring of environmental loads due to traffic and/or microseisms. A series of nondestructive testing methods (sonic tomography and radar investigation) have been used to assess the material properties, the internal cracking and the hinges status. The numerical analysis of the obelisk has been performed knowing the differences between the mechanical characteristics of 4 representative zones by means of a parametric analysis with respect to the mechanical characteristics of the undamaged section.
References
[1] G. De Canio, “Large Scale experimental facilities at ENEA for seismic tests on structural elements of the historical/monumental cultural Heritage”, Proc. 9th Int. Congress on Deterioration and Conservation of Stone, Venice 1924 June 2000.
[2] Marialuisa Mongelli: ”Analisi agli elementi finiti dell’Obelisco Lateranense di Piazza San Giovanni in Laterano a Roma” doc. ENEART3407G.
[3] De Canio, G. Fraraccio, M. Mongelli, N. Ranieri “Monitoraggio delle vibrazioni naturali ed indotte dal traffico”, Doc. ENEA RT45/08.
[4] A. Tatì “Indagine diagnostica tramite esame sonico e ricostruzione tomografica dell’Obelisco di San Giovanni in LateranoRoma”, Rapporto ENEA RT35/07.
[5] Paola Giaquinto: ”L’Obelisco Lateranense: Ricerche storicocritiche e cronologia degli avvicendamenti tecnologicocostruttivi”, Rep. ENEART3207.
[6] Paola Giaquinto, Alessandro Colucci: ”L’Obelisco Lateranense: Rilevazioni Georadar. Risultati preliminari”, Rep ENEART3607.
[7] G. Zingone, G. De Canio, G. Cavalieri, “On the improvement of monumental structure safety: a case study”, III European Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering, Lisbon, Portugal, 58 June 2006 C.A. Mota Soares et al. (eds.).
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Massimiliano Baldini, Stefano Bonifazi, Alessandro Colucci, Gerardo De Canio, Francesco Di Biagio, Marialuisa Mongelli, Angelo Tatì  ENEA, Unità Tecnica Tecnologie dei Materiali