Behavior of the Leaning Tower of Pisa: Analysis of Experimental Data from Structural Dynamic Monitoring

Abstract

Understanding the structural behavior of heritage buildings is usually a very complicated task because they typically present complex deterioration and damage patterns which cannot be fully evaluated by means of visual inspections. Moreover, the reliability of such constructions largely depends on different materials, structural components and details, the health of which is often unknown or affected by great uncertainties. In this regard, the experimental dynamic testing of heritage buildings and monuments subjected to ambient vibrations has become a valuable tool for their assessment because of the minimum interference with the structure. Traffic-induced vibrations are not always a feasible dynamic load for monumental buildings due to their very low intensity or owing to existing restrictions to road and rail traffic. On the other hand, the analysis of the experimental response under earthquakes can lead to more relevant information about the dynamic behavior of historic constructions, provided that the structure is equipped with a permanent sensor network. Within this framework, the present work illustrates preliminary results carried out from time and frequency domain analyses performed on the experimental dynamic response of the leaning tower of Pisa using seismic records. The main dynamic features of the monument have been identified, and then examined taking into account the seismic input and the soil-foundation-structure interaction.

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BEHAVIOR OF THE LEANING TOWER OF PISA: ANALYSIS OF
EXPERIMENTAL DATA FROM STRUCTURAL DYNAMIC
MONITORING
Raffaello BARTELLETTI
Full Professor
University of Pisa
Via Diotisalvi 2, 56126 Pisa , Italy
r.bartelletti@ing.unipi.it
Gabriele FIORENTINO
PhD Student
Department of Architecture, Roma Tre University
Largo Giovanni Battista Marzi, 10, 00153 Roma
gabriele.fiorentino@uniroma3.it
Giuseppe LANZO
Associate Professor
Department of Structural and Geotechnical Engineering, Sapienza University of Rome
Via Gramsci 53, 00197 Rome
giuseppe.lanzo@uniroma1.it
Davide LAVORATO
Research Fellow
Department of Architecture, Roma Tre University
Largo Giovanni Battista Marzi, 10, 00153 Roma
davide.lavorato@uniroma3.it
Giuseppe Carlo MARANO
Associate Professor
Department of Science of Civil Engineering and Architecture, Technical University of Bari
Via Orabona 4, 70125 Bari, Italy
giuseppecarlo.marano@poliba.it
Giorgio MONTI
Full Professor
Department of Structural and Geotechnical Engineering, Sapienza University of Rome
Via Gramsci 53, 00197 Rome
giorgio.monti@uniroma1.it
Camillo NUTI
Full Professor
Department of Architecture, Roma Tre University
Largo Giovanni Battista Marzi, 10, 00153 Roma
Visiting Professor at Fuzhou University, Fuzhou, Fujian 350108, China
camillo.nuti@uniroma3.it
Giuseppe QUARANTA
Assistant Professor
Department of Structural and Geotechnical Engineering, Sapienza University of Rome
Via Eudossiana 18, 00184 Rome, Italy
giuseppe.quaranta@uniroma1.it

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Nunziante SQUEGLIA
Assistant Professor
Univesity of Pisa
Via Diotisalvi 2, 56126 Pisa, Italy
squeglia@ing.unipi.it
Abstract
Understanding the structural behavior of heritage buildings is usually a very complicated task
because they typically present complex deterioration and damage patterns which cannot be
fully evaluated by means of visual inspections. Moreover, the reliability of such constructions
largely depends on different materials, structural components and details, the health of which
is often unknown or affected by great uncertainties. In this regard, the experimental dynamic
testing of heritage buildings and monuments subjected to ambient vibrations has become a
valuable tool for their assessment because of the minimum interference with the structure.
Traffic-induced vibrations are not always a feasible dynamic load for monumental buildings
due to their very low intensity or owing to existing restrictions to road and rail traffic. On the
other hand, the analysis of the experimental response under earthquakes can lead to more
relevant information about the dynamic behavior of historic constructions, provided that the
structure is equipped with a permanent sensor network. Within this framework, the present
work illustrates preliminary results carried out from time and frequency domain analyses
performed on the experimental dynamic response of the leaning tower of Pisa using seismic
records. The main dynamic features of the monument have been identified, and then
examined taking into account the seismic input and the soil-foundation-structure interaction.
Keywords: Leaning tower, Seismic monitoring, Signal processing, Soil-foundation-structure
interaction, Wavelets.
1. Introduction
The experimental assessment through dynamic monitoring has proved to be a reliable way for
enhancing the assessment of heritage buildings and monuments. Nowadays, the analysis of
the recorded dynamic response under ambient or forced vibrations is frequently adopted to
complement numerical studies. In this field, typical applications deal with the experimental-
based analysis of the global dynamic behaviour, the evaluation of the structural integrity or
the calibration of numerical models. Several implementations of structural dynamic
monitoring techniques to the analysis of historical constructions can be found in the current
literature, see for instance [1-6]. This paper presents the current efforts aimed at updating and
possibly improving the knowledge about the dynamic behaviour of the leaning tower of Pisa.
While this work is concerned with the analysis of the tower’s response under seismic loading,
a companion paper [7] is also presented with insights on seismic input and soil-foundation-
structure modelling. The tower height is 58.4 m from the foundation level (the height from the
ground is about 55 m) and it is known worldwide for its unintended tilt. The tower’s tilt began
during construction (work on the ground floor started on 1173) and increased in the decades
before the structure was completed. The inclination gradually increased until the structure was
stabilized. Stabilization procedures were concluded on 2002, and they reduced tower’s tilt of
0.54°. To date, the tower’s tilt with respect to the vertical direction is about 5.5° (the tower is
inclined along the North-South direction whereas a modest tilt angle exists along the East-
West direction). Details about the permanent sensor network for seismic monitoring installed
on the tower are first presented in this paper. Once the seismic events under consideration are

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listed, the corresponding recorded tower’s response is analysed, both, in time and frequency
domain.
2. Sensor network layout and selected seismic events
2.1 Seismic monitoring sensor network
The tower is equipped with a permanent sensor network basically intended for seismic
monitoring applications. The uni-axial accelerometer EpiSensor FBA ES-U and the three-
axial accelerometer EpiSensor FBA ES-T produced by Kinemetrics Inc. were adopted, and
their main properties are listed in Table 1.
Table 1. Summary of the main parameters of the sensors.
Parameter Value
Sensor type Force-balance accelerometer
No. of axes 1 (uni-axial sensor) or 3 (three-axial sensor)
Full-scale range User selectable at ± 0.25g, ± 0.5g, ± 1g, ± 2g or ± 4g
Bandwidth DC to 200 Hz
Dynamic range About 155 dB
A total of four measurement points are available on the tower, see Figure 1. Measurement
points in S1, S2 and S3 were equipped with a three-axial accelerometer. Axes were oriented
along the East (E), North (N) and vertical (V) direction. An uni-axial accelerometer is
available in S4, with its axis oriented along the vertical direction (V).
Figure 1. Approximate position of the accelerometers on the tower (left) and of the accelerometer on the
ground (right).
Besides the sensors installed on the tower, the dynamic monitoring network is also provided
with a three-axial accelerometer on the ground (Figure 1). This sensor was originally intended
for free-field recordings of the seismic input acting at the ground of the tower. However, its
position is very close to the tower’s foundation, and thus it is affected by the perturbations
induced on the free-field motion by the radiation of the structure. It is pointed out that this

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sensor on the ground does not work since 2012. The dynamic response of the tower is
recorded using a cyclic buffer with pre-defined length and user-selectable triggering
threshold. The operative parameters of the network are given in Table 2.
Table 2. Summary of the operative parameters of the sensor network.
Parameter Value
Selected full-scale range ± 0.25g
Accelerometer sensitivity 10 V/g
Full-scale range User selectable at ± 0.25g, ± 0.5g, ± 1g, ± 2g or ± 4g
Low-pass filter 100 Hz
High-pass filter 0.08 Hz
Theoretical dynamic range About 90 dB
Resolution 16 bit
Sampling frequency 400 Hz
2.2 Selected seismic events
The analysis of the seismic response of the tower is performed for the seismic events listed in
Table 3. These events span from 2004 to 2015.
Table 3. List of the considered seismic events.
Event label Date
Magnitude M
W
Distance from Pisa
150100023 2015-01-23 4.3 74
12010022 2012-01-27 5 94
12010015 2012-01-25 Not available Not available
060400070 2006-04-17 4.2 33
050500025 2005-05-17 4 16
041100050 2004-11-24 5.06 214
3. Analysis of the seismic response of the tower
3.1 Time and frequency analysis
For the sake of conciseness, only a few of time and frequency domain results are presented in
the following. The maximum recorded response (corresponding to the seismic events in Table
3) is provided in Table 4. It can be observed that the dynamic excitation level is rather modest,
being the maximum recorded acceleration value about 8 mg.
Table 4. Maximum recorded acceleration values.
Seismic event
Maximum acceleration Channel
150100023 0.01964 m/s
2
S3-N
12010022 0.0408 m/s
2
S3-E
12010015 0.0524 m/s
2
S3-N
060400070 0.06686 m/s
2
S3-E
050500025 0.02231 m/s
2
S3-E
041100050 0.08431 m/s
2
S3-E
The recorded response for the seismic event 12010022
is shown in Figure 2. The Fast Fourier
Transform (FFT) is performed after Hann-based windowing for leakage reduction. The

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frequency content of the recorded response for the seismic event 12010022 is shown in Figure
3. The Continuous Wavelet Transform (CWT) and the Wavelet Cross Spectrum (WCS) of
some signals are shown in Figure 4, Figure 5 and Figure 6.
Figure 2. Recorded tower response at S1, S2 and S3 under the seismic event 12010022.
Figure 3. FFT of the recorded tower response at S1, S2 and S3 under the seismic event 12010022.

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Figure 4. CWT of the recorded tower response at S3 under the seismic event 12010022.
Figure 5. WCS of the recorded tower response at S1, S2 and S3 along the East direction under the seismic
event 12010022.

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Figure 6. WCS of the recorded tower response at S1, S2 and S3 along the vertical direction under the
seismic event 12010022.
3.2 Identified natural frequencies
The fundamental (bending) mode of the tower has a natural frequency close to 1 Hz (Table 5).
Table 5. Natural frequency of the fundamental mode along the two directions.
Reference
North-South direction East-West direction
Nakamura et al. [8] 0.98 Hz 1.06 Hz
Macchi and Ghelfi [9] 1.08 Hz
Castellaro e Mulargia [10] 1 Hz 1.1 Hz
Atzeni et al. [11] 1.01 Hz 1.04 Hz
This study (S3-N, S3-E)
0.96 Hz 1.02 Hz
With the possible exception of Ref. [9], all the existing studies indicate that the natural
frequency of the fundamental mode is slightly less along the North-South direction than along
the East-West direction. This is probably caused by the tower’s tilt, which is predominant in the
North-South direction. The list of the identified natural frequencies is given in Table 6.
Table 6. Identified natural frequencies of the tower and comparison with existing studies.
This study
Nakamura et al. [8] Macchi and Ghelfi [9] Castellaro e Mulargia [10]
0.96 Hz 0.98 Hz 1.08 Hz 1 Hz
1.02 Hz 1.06 Hz 6.20 Hz 1.1 Hz
2.97 Hz 3 Hz 6.80 Hz 6.5 Hz
6.29 Hz 6.3 Hz 13.88 Hz 6.7 Hz
14 Hz
Results in Table 6 show a good agreement between this study and the existing ones.
Remarkably, only this study and Ref. [8] have identified the vertical mode of the tower. The
natural frequency of the vertical mode is about 3 Hz.

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3.3 Rocking of the tower foundation
The rocking of the tower foundation can be assessed by filtering the acceleration time histories
recorded in S1-V and S4-V within the frequency band of the mode of interest. Figure 7 shown
the filtered time histories recorded in S1-V and S4-V for the seismic event 12010022, so as to
isolate the contribution of the fundamental mode. Figure 8 shown the same time histories
filtered in such a way to isolate the contribution of the vertical mode.
Figure 7. Butterworth band-pass filter of the tower response recorded at S1-V and S4-V during the seismic
event 12010022. The filter is intended to isolate the dynamics attributable to the first fundamental mode.
Figure 8. Butterworth band-pass filter of the tower response recorded at S1-V and S4-V during the seismic
event 12010022. The filter is intended to isolate the dynamics attributable to the vertical mode.
These results clearly indicate that the vertical mode of the tower occurs with no base rocking.
On the contrary the fundamental mode causes a significant rocking of the foundation.

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3.4 Inter-event assessment of the fundamental natural frequencies
Table 7 presents the natural frequencies of the fundamental mode along the two directions for
all the selected seismic events.
Table 7. Natural frequency of the fundamental mode along the two directions for different seismic events.
Seismic event
North-South direction East-West direction Groundwater level
150100023
1.01 1.06 Not available
12010022
0.96 1.02 Not available
12010015
1.00 1.05 Not available
060400070
0.99 1.01 1.85 m a.m.s.l
050500025
0.99 1.05 1.79 m a.m.s.l
041100050
1.00 1.01 1.98 m a.m.s.l
The results in Table 7 demonstrate that the natural frequency of the fundamental mode does not
change significantly. For all events, however, the natural frequency along the North-South
direction is slightly less than the one identified along the East-West direction. The existence of a
drainage system contributes to the mitigation of the groundwater level oscillations.
4. Conclusions
This paper presented preliminary results about the time and frequency domain analysis of the
experimental seismic response of the leaning tower of Pisa. To this end, some seismic events
spanning from 2004 to 2015 have been considered. Because of its inclination, the natural
frequency of the fundamental mode is slightly less along the North-South direction than along
the East-West direction. Differently from the vertical mode, the fundamental bending mode
causes a significant rocking of the tower’s foundation and its natural frequency value does not
seem subjected to significant variations. Current efforts aim at enhancing the existing sensor
network by adding more measurement points. Further experimental tests are under
consideration for better assessing local amplification effects of the seismic excitation.
5. Acknowledgements
The authors would like to acknowledge the Opera della Primaziale Pisana for having promoted
and supported this study. Special thanks go to Professor Luca Sanpaolesi for having provided
insights and expertise during the period of the research.
6. References
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the “Saint Andrea” Masonry Bell Tower in Venice. A new method for the determination
of “Tower Global Young’s Modulus E”, Engineering Structures, Vol. 32, No. 2,
February 2010, pp. 353-360.
[2] BARTOLI, G., BETTI, M., GIORDANO, S., “In situ static and dynamic investigations
on the “Torre Grossa” masonry tower”, Engineering Structures, Vol. 52, July 2013, pp.
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on the optimal sensor placement for historic swing bridge dynamic monitoring",

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