“EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON THE SEISMIC BEHAVIOUR OF THE SAN FREDIANO BELL TOWER IN LUCCA„

This paper presents a study on the seismic response of the San Frediano bell tower in Lucca. The tower’s ambient vibrations were con− tinuously monitored for about one year, from October 2015 to October 2016. During this monitoring campaign, many seismic events were recorded on the tower and the most relevant turned out to be the Amatrice earthquake, which struck Central Italy on 24 August 2016. The paper begins with a review of the experimental results obtained. Then, a finite element numerical model of the tower is presented and validated via model updating, by assuming the tower’s constituent materials to be unable to withstand tensile stresses. The exper− imental records of the Amatrice earthquake are also included in the analysis to assess the dynamic behaviour of the finite element model under ambient vibrations. Finally, a numerical simulation is performed of the tower subjected to the Lunigiana earthquake, recorded in Fivizzano (Tuscany) on 21 June 2013: the results of the dynamic analysis are presented and discussed. al., 2012; Bartoli et al., 2013; Sabia et al., 2015; De Ste− fano et al., 2016; Ferraioli et al., 2017; de Silva et al., 2018], even in the presence of structural damage [Pineda et al., 2011; Zanotti Fragonara et al., 2017; Pel− legrini et al., 2018]. The literature contains many contributions regard− ing the seismic vulnerability of age−old masonry tow− ers, underscoring the importance of the issue. Moreover, recent seismic events in Northern and Cen− tral Italy, such as the Emilia earthquake (2012) and the Amatrice earthquake (2016) involved many historic masonry towers and pose important questions on the assessment of such structures under seismic actions. In light of the Italian [D.M. 2018; D.P.C.M. 2011] and international regulations, the most often used method− ology in the literature relies on the use of equivalent static actions and pushover analyses. In Bernardeschi et al., [2004] the seismic load is modeled via static equiv− alent loads and a nonlinear analysis is performed, by using the constitutive equation of masonry-like mate− rials [Lucchesi et al., 1994] in order to reproduce the actual crack pattern in the structure. With regard to the application of pushover analysis for the seismic as− sessment of masonry towers, some recent studies pro− vide high detailed discussion of the methodology used [Resta et al., 2013; Cattari et al., 2014; Preciado, 2015; Valente and Milani, 2016b; Cakir et al., 2016; Boccia− relli and Barbieri, 2017; Bartoli et al., 2017; Shayka et al., 2018]. The seismic vulnerability of masonry towers has also been investigated via fully dynamic analysis [Clough and Penzien, 1975], which consists in the nu− merical integration of the equations of motion result− ing from FE discretisation of the construction subjected to artificial or real time−histories of acceleration/ve− locity/displacement. The choice of the constitutive equation to realistically model the mechanical behav− iour of the towers is of crucial importance: in fact, be− cause of masonry’s inability to withstand tensile stresses and large compressive stresses, ancient towers may exhibit damage due to the only permanent loads. This nonlinear behaviour strongly influences the tow− ers’ response to dynamic actions, which linear elastic constitutive laws are unable to predict. Some first attempts to study the dynamic behaviour of masonry towers through numerical tools are shown in [Casolo, 1998; Lucchesi and Pintucchi, 2007], where numerical procedures have been implemented by using one−dimensional finite elements and ad – hoc consti− tutive laws. In Callieri et al., [2010] the mechanical be− haviour of the San Gimignano “Rognosa” tower subjected to a natural accelerogram is studied via the masonry-like constitutive equation. Lourenço et al., [2009] shows an application to a minaret in India, and Bayaktar et al. [2010] presents a nonlinear dynamic analysis of the Haghia Sophia bell tower in Trabzon, Turkey. Both these applications rely on the use of non− linear constitutive laws implemented whitin commer− cial codes. More recently, numerous papers have been devoted to investigating the dynamic behaviour of ma− sonry towers under seismic loads with particular re− gard to northern Italy [Milani et al., 2012; Casolo and al., 2013; Acito et al., 2014; Minghini et al., 2014; Va− lente et al., 2016a; Castellazzi et al., 2018; D’Altri et al., 2018; Karanikoloudis et al., 2018]: these papers focus on the comparison of the results obtained via fully dy− namic and pushover analyses. This paper presents the experimental and numerical investigations performed on the dynamic behaviour of the San Frediano bell tower, located in the historic centre of Lucca (Italy). The ambient vibrations of the tower, instrumented with four tri−axial seismometric stations, have been continuously monitored from 28 October 2015 to 16 October 2016. The accuracy of the measurement de− vices and the availability of powerful system identifi− cation algorithms allowed a great deal of information to be collected on both the tower’s dynamic behaviour and its dependence on environmental parameters, such as temperature [Azzara et al. 2018]. On 24 August 2016, at 01:36 a.m. (UTC), the signal of the Mw 6.0 Amatrice earthquake was detected and recorded on the tower. Although the epicentral distance is about 400 km from Lucca, the earthquake signal was clearly revealed by the sensors, with velocities at the tower’s top on the same order of magnitude as those induced by the swinging of the bells. The results of the monitoring campaign, with particular focus on the signals from the seismic event recorded on the tower, are reported in Section 2. Section 3 is instead devoted to the numerical mod− elling of the tower’s dynamic behaviour. Briefly, the modelling procedure is as follows. The mechanical properties of the tower’s constituent materials are first obtained via FE model updating: in particular, a nu− merical procedure, based on linear perturbation and modal analysis, is adopted, which allows taking into account the effects of masonry’s weak tensile strength on the modal properties of the structure [Girardi et al., 2018]. Then a FE numerical simulation is performed by as− signing to the tower model the signal of the Amatrice earthquake recorded at the base of the structure: the experimental and numerical results are compared.


INTRODUCTION
Ancient masonry towers, which constitute an im− portant part of the Italian architectural heritage, gen− erally exhibit high sensitivity to dynamic actions, such as ambient vibrations, bell swinging, etc. For this rea− son, continuous long−term vibration monitoring rep− resents an effective non−destructive technique to investigate and check the dynamic behaviour and the health status of such structures [Azzara et al., 2014]. In fact, changes in their modal properties (natural fre− quencies, mode shapes and damping ratios) can repre− sent effective damage indicators, as described in [Gentile and Saisi, 2007;Masciotta et al., 2017;Uber− tini et al., 2018;Azzara et al., 2018]. Moreover, the structural scheme of masonry towers is generally sim− ple, and the use of finite element (FE) model updating techniques allows obtaining useful information on the boundary conditions and mechanical properties of their constituent materials [Júlio et al., 2008;D'Ambrisi et al., 2012;Bartoli et al., 2013;Sabia et al., 2015;De Ste− fano et al., 2016;Ferraioli et al., 2017;de Silva et al., 2018], even in the presence of structural damage [Pineda et al., 2011;Zanotti Fragonara et al., 2017;Pel− legrini et al., 2018].
The literature contains many contributions regard− ing the seismic vulnerability of age−old masonry tow− ers, underscoring the importance of the issue. Moreover, recent seismic events in Northern and Cen− tral Italy, such as the Emilia earthquake (2012) and the Amatrice earthquake (2016) involved many historic masonry towers and pose important questions on the assessment of such structures under seismic actions.
In light of the Italian [D.M. 2018; D.P.C.M. 2011] and international regulations, the most often used method− ology in the literature relies on the use of equivalent static actions and pushover analyses. In Bernardeschi et al., [2004] the seismic load is modeled via static equiv− alent loads and a nonlinear analysis is performed, by using the constitutive equation of masonry-like mate− rials [Lucchesi et al., 1994] in order to reproduce the actual crack pattern in the structure. With regard to the application of pushover analysis for the seismic as− sessment of masonry towers, some recent studies pro− vide high detailed discussion of the methodology used [Resta et al., 2013;Cattari et al., 2014;Preciado, 2015;Valente and Milani, 2016b;Cakir et al., 2016;Boccia− relli and Barbieri, 2017;Bartoli et al., 2017;Shayka et al., 2018].
The seismic vulnerability of masonry towers has also been investigated via fully dynamic analysis [Clough and Penzien, 1975], which consists in the nu− merical integration of the equations of motion result− ing from FE discretisation of the construction subjected to artificial or real time−histories of acceleration/ve− locity/displacement. The choice of the constitutive equation to realistically model the mechanical behav− iour of the towers is of crucial importance: in fact, be− cause of masonry's inability to withstand tensile stresses and large compressive stresses, ancient towers may exhibit damage due to the only permanent loads. This nonlinear behaviour strongly influences the tow− ers' response to dynamic actions, which linear elastic constitutive laws are unable to predict.
Some first attempts to study the dynamic behaviour of masonry towers through numerical tools are shown in [Casolo, 1998;Lucchesi and Pintucchi, 2007], where numerical procedures have been implemented by using one−dimensional finite elements and ad -hoc consti− tutive laws. In Callieri et al., [2010] the mechanical be− haviour of the San Gimignano "Rognosa" tower subjected to a natural accelerogram is studied via the masonry-like constitutive equation. Lourenço et al., [2009] shows an application to a minaret in India, and Bayaktar et al. [2010] presents a nonlinear dynamic analysis of the Haghia Sophia bell tower in Trabzon, Turkey. Both these applications rely on the use of non− linear constitutive laws implemented whitin commer− cial codes. More recently, numerous papers have been devoted to investigating the dynamic behaviour of ma− sonry towers under seismic loads with particular re− gard to northern Italy [Milani et al., 2012;Casolo and al., 2013;Acito et al., 2014;Minghini et al., 2014;Va− lente et al., 2016a;Castellazzi et al., 2018;D'Altri et al., 2018;Karanikoloudis et al., 2018]: these papers focus on the comparison of the results obtained via fully dy− namic and pushover analyses.
This paper presents the experimental and numerical investigations performed on the dynamic behaviour of the San Frediano bell tower, located in the historic centre of Lucca (Italy).
The ambient vibrations of the tower, instrumented with four tri−axial seismometric stations, have been continuously monitored from 28 October 2015 to 16 October 2016. The accuracy of the measurement de− vices and the availability of powerful system identifi− cation algorithms allowed a great deal of information to be collected on both the tower's dynamic behaviour and its dependence on environmental parameters, such as temperature [Azzara et al. 2018]. On 24 August 2016, at 01:36 a.m. (UTC), the signal of the Mw 6.0 Amatrice earthquake was detected and recorded on the tower. Although the epicentral distance is about 400 km from Lucca, the earthquake signal was clearly revealed by the sensors, with velocities at the tower's top on the same order of magnitude as those induced by the swinging of the bells. The results of the monitoring campaign, with particular focus on the signals from the seismic event recorded on the tower, are reported in Section 2.
Section 3 is instead devoted to the numerical mod− elling of the tower's dynamic behaviour. Briefly, the modelling procedure is as follows. The mechanical properties of the tower's constituent materials are first obtained via FE model updating: in particular, a nu− merical procedure, based on linear perturbation and modal analysis, is adopted, which allows taking into account the effects of masonry's weak tensile strength on the modal properties of the structure .
Then a FE numerical simulation is performed by as− signing to the tower model the signal of the Amatrice earthquake recorded at the base of the structure: the experimental and numerical results are compared.
Lastly, the tower model is subjected to the accelero− gram recorded in Fivizzano on 21 June 2013 at 10:33 a.m. (UTC), during the Mw 5.1 Lunigiana earthquake. Fivizzano is about 50 km from Lucca, and the Peak Ground Acceleration (PGA) of the event was 1.38 m/s 2 . The effects of the accelerogram on the tower are then addressed.
The FE model updating and dynamic analysis are performed via the NOSA−ITACA code [Binante et al. 2017;Degl'Innocenti et al., 2006;Padovani et al., 2008], a FE software implemented by the Mechanics of Materials and Structures laboratory of ISTI−CNR, to which the authors belong. The software has been specifically developed for the structural analysis of an− cient masonry constructions.
The novelty of the paper relies on the twofold ex− ploitation of the experimental data recorded on the tower. On the one hand, they are used to conduct a nonlinear model updating, on the other, they are com− pared with the numerical results of the updated FE model subjected to the Amatrice earthquake recorded in Lucca. In this way, the experimental results turn out to be useful not only to build a realistic FE model of the tower, but also for validating the numerical method implemented in NOSA−ITACA, with particular regard to the tower's response to ambient vibrations.

THE EXPERIMENTAL CAMPAIGN AND THE AMATRICE EARTHQUAKE
The Basilica of San Frediano (see Figure 1) dates back to the 11 th century and the church's bell tower ( Figure 2) is one of the best preserved in the Lucca's historic centre. The geometry of the tower is illustrated in Figure 3. It is 52 m high, with walls varying in thick− ness from about 2.1 m at the base to 1.6 m at the top. The tower is entered through a masonry staircase lead− ing from the street level to the first floor, which is formed by a masonry vault set at a height of about 8.6 m. From this level, a stone staircase running along the inner perimeter provides access to the terminal section of the tower, at a height of about 40 m, which houses the bells ( Figure 4). The bell chamber is separated from the rest of the structure by a stiff masonry vault, rein− forced with 4 rectangular cross section steel tie rods. At about 43 m, a walkable wooden floor overlies the vault and serves to allow access to the bells. The tower's walls have openings, in various ornate windows, on all sides. It is covered by a pavilion roof made up of wooden trusses and rafters in a very poor state of maintenance.
No rigid diaphragms are present inside the tower be− tween the two vaults. The San Frediano Basilica adjoins the tower on two sides for about 13 m of its height.
With regard to the tower's constituent materials, on vi− sual inspection, the masonry appears to be made of reg− ular stone blocks at the base, while quite homogeneous brick masonry is visible in the upper section, apart from the central part of the walls, where the masonry be− tween the windows is made up of stone blocks.
Between May and June 2015, the tower was instru− mented with four SARA (www.sara.pg.it) tri−axial seis− mometric stations ( Figure 5). Each station was equipped with a SL06 24−bit digitizer coupled to a SS20 seis− mometer (electrodynamic velocity transducer, 2.0 Hz eigenfrequency), made available by the Arezzo Seis− mology Observatory (INGV). The instruments were arranged on the San Frediano bell tower along a verti− cal line, as shown in layout L1 of Figure 6, and left ac− tive on the tower for five days. The results of this experiment are reported in [Azzara et al. 2016; Barsoc−      [Azzara et al. 2018]. Over the course of this year, two main sensor layouts were chosen. In the first (reported as L2 in Figure 6), two sen− sors were placed on two opposite sides of the bell chamber, and the remaining aligned along the tower. In the second (reported as L3 in Figure 6), one of the sen− sors along the tower's height was moved to the base, in order to measure ground vibrations. It was in this lay− out that the Amatrice seismic sequence was recorded on 24 August 2016. In all the experiments the sampling frequency was set to 100 Hz. Data from the sensors have been analysed via the MACEC code [Reynders et al., 2014], in which the Covariance Driven Stochastic Sub− space Identification method (SSI/Cov) [Brincker and Ventura, 2015;Reynders et al., 2016], amongst others, is implemented. The data have been split into different records, each one hour long, and analyzed separately. The parameters used in the analyses are: the number of block rows in the correlation matrix, set to 100, and the number of data blocks for evaluating the variance of the output correlation estimates, set to 200. Table 1 re− ports the mean values, evaluated in August 2016, of the first five frequencies identified and their corresponding damping ratios. The first two frequencies correspond to flexural mode shapes, the first along the X direction and the second along Y. The third frequency appears along both the X and Y directions: it likely relates to a torsional mode shape. The last two frequencies corre− spond once again to flexural model shapes. More details on mode shapes are given in [Azzara et al. 2018]. Figure 7 shows the plot of a typical time history of the accelerations recorded on the tower: the accelera− tion level is very low, on the order of 5·10 −4 m/s 2 . How− ever, important variations in the acceleration levels were observed during the study period, with peaks of up to 3·10 −2 m/s 2 , corresponding to the swinging of the FIGURE 7. Acceleration in the X direction recorded by a sensor on the bell chamber (+42 m), 1 August, 2016 at 11:00 UTC.
FIGURE 8. Amatrice earthquake. Acceleration in X direction at the base (cyan) and at the level of the bell chamber (red).

FIGURE 9.
Amatrice earthquake. Acceleration in the Y direction at the base (cyan) and at the level of the bell cham− ber (red). bells and the more trafficked hours of the day, as well as to the Amatrice earthquake.
On 24 August 2016, at 1:36 a.m. (UTC), the seismic sequence from the Amatrice earthquake, which hit cen− tral Italy with Mw 6.0 and PGA of 8.5 m/s 2 (recorded at the Amatrice site), was also recorded on the tower. Al− though Lucca is about 400 km from Amatrice, the earthquake signal was clearly detected by the sensors, with velocities on the same order of magnitude as those induced by the swinging of the bells. No significant damage was observed on the tower.
Figures 8 to 10 report the X, Y and Z accelerations recorded at the base (cyan) and at the top (red) of the bell tower on 24 August 2016, at the time of the Amatrice earthquake. Strong amplification of the signal along the tower's height can be observed, particularly in the hor− izontal directions, along which the signal at the top of the tower is more than 5 times that recorded at the base.
The maximum ground acceleration recorded at the base of the tower is on the order of 5·10 −3 m/s 2 , while the maximum value recorded at the top is 3.9·10 −2 m/s 2 . The Fast Fourier Transforms (FFT) of the accelerations at the base and the top are shown in the Figures 11, 12 and 13. The tower's natural frequencies, reported in Table 1, are highlighted by the earthquake and can be clearly iden− tified in the figures. No significant changes in the tower's natural frequencies and in its damping ratios were found after the seismic event [Azzara et al., 2018].

NUMERICAL MODELLING OF THE TOWER'S DY-NAMIC BEHAVIOUR
A widely adopted constitutive equation which de− scribes the mechanical behaviour of masonry materi− als models them as nonlinear elastic materials with low tensile strength σ t > 0 and finite compressive strength σ c < 0 [Lucchesi et al., 2008]. This constitu− tive equation is able to take into account some of ma−

Frequency [Hz] Damping [%]
Mode 1 (Bending X) sonry's peculiarities, in particular its inability to with− stand large tensile stresses. Assumptions underlying the model are that the infinitesimal strain tensor E is the sum of an elastic part E e , a fracture part E f and a crushing part E c , and that the stress tensor T, whose eigenvalues belong to the interval [σ c σ t ], depends linearly and isotropically on the elastic part. The frac− ture strain and the crushing strain are respectively positive−semidefinite and negative− semidefinite and satisfy suitable orthogonality conditions involving the stress, which turns out to be a nonlinear function of the infinitesimal strain. This constitutive equation generalizes the equation of masonry-like or no-tension materials described in Del Piero, [1989] and Di Pasquale, [1992] and has been implemented within the non−commercial FE software NOSA−ITACA Binante et al., 2017] developed and freely distributed by ISTI−CNR (www.nosaitaca.it). NOSA−ITACA, aimed at the static and dynamic analysis of masonry buildings, is the re− sult of the integration of the FE code NOSA into the open−source SALOME platform (http://salome−plat− form.org). NOSA−ITACA moreover provides for the modal analysis of linear elastic [Porcelli et al., 2015] and masonry  structures.
This section is devoted to the numerical modeling of the bell tower's dynamic behaviour. All numerical analyses presented in this paper have been conducted via the NOSA-ITACA code, already employed for dy− namic analyses of the "Rognosa" tower [Callieri et al., 2010] and the Maddalena bridge in the Lucca territory [De Falco et al., 2014].
The San Frediano bell tower has been discretised into 18,645 thick shell and beam elements (element n. 10 and 9 in Binante et al., [2017] with 113,538 degrees of freedom, as shown in Figure 14. Beams have been used to model the steel tie rods and wooden elements of the roof. Using shell elements made up of layers with different thicknesses and materials allows a de− tailed modelling of the walls geometry and, at the same time, reduces the computational cost of the dy− namic analysis.
The masonry has been modelled as a homoge− neous material with Poisson's ratio n = 0.2, mass density ρ = 2000 kg/m 3 , and compressive strength σ c = -1.23 MPa. Young's modulus E and the tensile strength σ t are unknown and can be determined via the model updating procedure adopted in . The structure is assumed to be clamped at its base, and additional fixed restraints have been imposed 12.50 m above the base to take into account for the church's adjacent walls.

FINITE ELEMENT MODEL UPDATING
FE model updating combines FE analysis and struc− tural health monitoring, in order to obtain information on the boundary conditions and the mechanical prop− erties of the structure's constituent materials. FE model updating consists of fine−tuning some of the model pa− rameters in order to minimize the distance between the numerical and experimental modal properties (natural frequencies and mode shapes). Girardi et al., [2018] describes the numerical proce− dure implemented in NOSA-ITACA: it is based on lin− ear perturbation and allows evaluating the natural frequencies and mode shapes of masonry buildings in the presence of cracks, thereby taking into account ma− sonry's nonlinear behaviour. The procedure consists of the following steps: (1) the initial loads and boundary conditions are applied to the FE model and the result− ing nonlinear equilibrium problem is solved through an iterative scheme. (2) a modal analysis about the equi− librium solution is performed, using the tangent stiff− ness matrix calculated in the last iteration before convergence is reached, thereby allowing to automati− cally take into account the effects of the stress distri− bution on the structure's stiffness. Within this frame− work, a model updating procedure aimed at matching the experimental and numerical frequencies (calculated after a perturbation analysis), allows for assessing the unknown parameters, such as the mechanical properties and boundary conditions. In the case of the San Fredi− ano bell tower, the global Young's modulus E and ten− sile strength σ t of the masonry, considered to be homogeneous in the model, have been updated in order to fit the tower's experimental frequencies. Table 2 re− ports the values calculated via the model updating pro− cedure in bold type (the mechanical properties of the wooden and steel elements respectively making up the roof and tie elements are also reported and taken as fixed during model updating). Table 3 instead shows a comparison between the numerical and experimental values of the tower's first four natural frequencies. The numerical procedure fits the first three mode shapes very well, while the fourth frequency, involving the higher order flexural mode shape along the X direction, is underestimated. The MAC (Modal assurance Criterion) between the numerical and experimental mode shapes is always over 0.9.

NUMERICAL DYNAMIC ANALYSIS: RECORD OF THE AMATRICE EARTHQUAKE AT THE TOWER BASE
The numerical model calibrated via the procedure de− scribed in the previous subsection has been subjected to accelerograms of different magnitude, in order to test the dynamic response of the tower to different excita− tion levels. The first test was conducted by using the ac− celerogram recorded by the authors at the base of the tower on 24 August 2016, corresponding to the 1:36 a.m. (UTC) Amatrice seismic sequence. After the dead loads were assigned, the seismic signal was applied to the model, whose numerical response to the dynamic exci− tation was then compared to that actually recorded on the tower. This provided a check of the numerical method implemented in NOSA−ITACA. The damping matrix adopted in the dynamic analysis has been calcu− lated according to the Rayleigh hypothesis [Clough and Penzien, 1975], using the experimental damping ratios measured on the tower for the first two mode shapes re− ported in Table 1, after averaging on the August 2016 records. The duration of the quaking was 200 s, and the time step for numerical integration was 0.04 s. Figure  15 shows the response of the top of the tower (at the level of the bell chamber, about +42 m) in the X direc− tion vs. time recorded by the instrument (red), together with that calculated by NOSA−ITACA (black).   in X direction vs. the corresponding experimental ones. The regression line is also plotted in the graph: the correlation between the two datasets is quite linear, as demonstrated by the high value of the correlation co− efficient. The slope of the regression line, however, in− dicates that on average the numerical response underestimates the actual accelerations recorded on the tower. Figures 17 and 18 show the tower's response along the Y direction. The correlation coefficient in Fig  near 1, indicating a very good correspondence between the numerical and experimental data, which is also ev− ident by the superposition of the time−histories. Fig−  ures 19 and 20 show the acceleration envelopes calculated along the tower's height in the horizontal di− rections, respectively for the southern and the eastern façade of the tower. The tower exhibits a rather linear amplification of the acceleration values in the X direc− tion, while amplification along Y is nonlinear, and de− spite the low values of the PGA applied at the base, the maximum acceleration at the tower top reaches about five times the value at the base: this finding is in good agreement with the experimental evidence. Table 4 summarizes the maximum acceleration values actually recorded by the instruments at the top and those eval− uated numerically via the NOSA−ITACA code. Also in this case, the agreement between the experimental re− sponse and the numerical simulation is very good in the Y direction, while the numerical model seems to un− derestimate the response along X.

NUMERICAL DYNAMIC ANALYSIS: RECORD OF THE FIVIZZANO EARTHQUAKE
The comparison between the numerical and exper− imental dynamic responses of the San Frediano bell tower shown in the previous subsection furnishes a val− idation of the tower's FE model under ambient vibra− tions, including far−field earthquakes. In order to investigate the effects of larger amplitude seismic events, the model has been subjected to the accelero− gram recorded at 10:33 a.m. (UTC) in the town of Fiviz− zano by the FIVI seismic station [Luzi et al., 2017], (itaca.mi.ingv.it) during the earthquake of 21 June 2013. Fivizzano is about 50 km from Lucca, in the area known as the Lunigiana and the effects of the seismic sequence were clearly felt in the city's historic centre.
The acceleration recorded by the FIVI station is shown in Figure 21, for the North−South and the East− West components, respectively. The PGA of the event was 1.38 m/s 2 , in the North−South direction. The am− plitudes have a similar order of magnitude in the two directions. The duration of the quaking was 12 s, and the time step for numerical integration was 0.005 s.  After application of the dead loads, the tower model was subected to the Fivizzano earthquake, considering the two directions of the accelerogram simultaneously. Figures from 22 onward show some results of the dynamic analysis. In particular, Figure 22 shows the FFT of the acceleration at the base and at the top of the tower, in the two horizontal directions. With respect to the Amatrice signal recorded at the tower's base (Fig−  ures 11, 12), the spectrum of the Fivizzano earthquake shows high−frequency content. The natural frequencies of the tower are highlighted by the tower's response. Figure 23 shows the maximum acceleration (with respect to time) computed by NOSA−ITACA vs. the tower's height, along directions X (cyan) and Y (red). It is worth noting that the diagrams' shapes are not lin− ear or monotonically increasing with the tower's height, as for the Amatrice earthquake (see Figures 19 and 20), but rather similar to a combination of the structure's highest mode shapes. Strong amplification of the ground accelerations appears in correspondence with the bell chamber. The maximum amplification is how− ever similar to that observed for the Amatrice record− ing: accelerations at the top are about 5 times those at the ground. With regard to the maximum displacements calculated along the tower's height, Figures 24 and 25 show these quantities evaluated in the middle (red dashed line) of the northern and western façade, re− spectively. The values reached at the top of the tower are modest in comparison to the tower's height, in agreement with the modest value of the peak ground acceleration, and irregularities in the diagrams are due to the presence of the openings along the façades.
The overall behaviour of the tower, with particular regard to the X direction, clearly enters the nonlinear field. This is confirmed by Figure 26, where the stress field σ zz at 3.16 s is plotted, and reveals a significant number of points at which the maximum compressive strength is reached, particularly the portions of masonry within the openings (corresponding to base and top of the pillars between the bifora and trifora windows). High values of compressive strength are also evident at the corners of the base section. Figure 27 shows a plot of the maximum eigenvalue of the crushing strain at E c 3.16 s. A time−history of the same quantity calculated at point A is instead plotted for the external (black) and the internal (red) layers in Figure 28. Fracture strains are depicted in Figure 29, where the maximum eigen− value of the fracture strain E f is plotted at 3.01 s, for both the external and internal layer. Fracture strains are visible in the spandrels of the windowed façades, giv− ing rise to diagonal cracks, in the tower's upper vault and the highest part of the structure.   tower, which is also in very poor state of maintenance.
In conclusion, despite satisfactory global behaviour of the tower under the seismic event, the numerical sim− ulation reveals local damage concentrated near the openings in the façades and in the vaults, and the high values of the accelerations affecting the upper part of the tower (bell chamber and merlons), which appears to be the most vulnerable to seismic actions.

CONCLUSIONS
This paper presents a detailed study on the seismic response of the San Frediano bell tower in Lucca, whose ambient vibrations were continuously monitored for about one year by the authors. The novelty of the paper relies on the twofold exploitation of the experimental data recorded on the tower. On the one hand, the ex− perimental results allowed building a realistic FE model of the tower via model updating procedures, on the other, the availability of the tower's experimental re− sponse to natural earthquakes, such as the Amatrice earthquake, allowed performing and validating the dy− namic simulations conducted via the FE code NOSA− ITACA. Lastly, the tower's response to the Fivizzano earthquake was simulated and analyzed, pointing out the sensitivity of the tower to such an excitation. The paper emphasizes the importance of both experimental measurements and numerical simulations in assessing the seismic behaviour of historic masonry buildings.