Massimiliano Ferraioli, Alberto Mandara. Department of ... of dynamic properties, together with site seismicity and ... of 1457. In the past, laboratory and on-site.
Dynamic identification and seismic safety of masonry bell towers
Massimiliano Ferraioli, Alberto Mandara Department of Civil Engineering, Second University of Naples, Via Roma 29, 81031Aversa, Italy.
Donato Abruzzese Department of Civil Engineering, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Roma.
Lorenzo Miccoli Division 7.1-Building Materials, BAM Federal Institute of Material Research and Testing, Berlin, Germany.
Keywords: Masonry towers, structural identification, model updating. ABSTRACT The paper addresses two case studies of structural monitoring and seismic assessment of medieval masonry towers in Italy: the bell tower of Aversa and the bell tower of Capua. These monuments in the Campania region were monitored by means of full-scale environmental vibration testing. Measured responses were then used for modal identification. The procedure is based on a typical finite element model updating technique based on vibration test results. Parameters optimization is carried out by minimizing a weighted error criterion relative to the building’s modal properties. A satisfactory improvement on modal parameters is thus obtained, resulting in a close agreement between the modal properties observed in dynamic tests and those calculated from numerical model. Seismic assessment is carried out with nonlinear static analysis of the tower under multimodal distributions of lateral loads. Nonlinear analysis indicates the potential collapse mechanisms and evidences dangerous structural weakness which may play a role in the seismic vulnerability of the towers.
1
INTRODUCTION
Many countries, especially in southern Europe, are greatly exposed to seismic hazard, which causes valuable building heritage to be high at risk of severe damage or even destruction when exposed to strong earthquake ground motions. The recent experience of Italian seismic events (Umbria and Marche 1997, Puglia and Molise 2002, Abruzzo 2009) provided wide observational information about the recurrent behaviour, the damage patterns and the intrinsic vulnerability of monumental buildings. This problem mostly stands for historical and monumental constructions, due to the fact that most of them frequently lack basic seismic features and/or were never fitted with adequate provisions against earthquake actions. This evidence, that confirms historical constructions to be by far the most vulnerable from the seismic point of view, demands for the definition of urgent strategies for the protection of cultural heritage from seismic hazard. Furthermore,
typical problems of masonry structures concern aspects like inherent structural lacks, material degradation, geotechnical problems, buckling behaviour of slender elements and dynamic loading vulnerability. The safeguard of these historical and monumental buildings from earthquakes would, in the first place, preserve human beings from a serious hazard to their own safety, but also of protecting unique art and architecture masterpieces from severe damage or even from destruction. The definition of reliable models and methods for seismic risk assessment of historical constructions is thus very interesting topic. A great number of studies in the literature are dedicated to destructive and non-destructive static and dynamic tests on masonry structures, to procedures for the identification of mechanical parameters as well as to calibration of the reliable structural models (Abruzzese et al. 2008, Bayraktar et al. 2009, Bennati et al. 2005, Bernardeschi et al. 2004, Carpinteri et al. 2005, De Sortis et al. 2005, Ivorra et al. 2006, Júlio e al. 2008, Peñaa et al. 2010). The main goal is a wide
knowledge of the structure to avoid inadequate, unsuitable or dangerous rehabilitation operations, and to select non-invasive and reversible techniques for the best exploitation of material and technology features. On the other hand, modelling the mechanical behaviour of masonry may play an important role, due to both inherent material complexity and great scatter in mechanical properties. The random character of masonry mechanical features, in fact, makes the prediction of structural risk quite critical. Effective procedures for the identification of the structural parameters from static and dynamic testing are thus required, and the effects of the random characteristics of masonry on the reliability of the results should be evaluated. In particular, dynamic measurements may be very useful for the identification of mechanical properties and soil restraints and, consequently, for the calibration of advanced numerical finite element models. In other words, the knowledge of dynamic properties, together with site seismicity and stratigraphy, is the starting point for an accurate estimation of the seismic safety of these structures. The current paper is dedicated to the experimental analysis and subsequent modelling of two towers dating back to the Middle Ages. In particular, the methodology defined to reach the goals aforementioned consisted of: 1) defining a finite element model of the towers; 2) defining localization and direction of the measurement points from modal analysis of the FEM model; 3) identifying mode shapes and frequencies, by environmental vibrations measurements; 4) calibrating a refined numerical model. 2
PRELIMINARY INVESTIGATIONS
Two bell towers are selected as representative samples of medieval masonry towers in the Campania region of Southern Italy. The bell tower of the Aversa Cathedral, in city centre of Aversa (Italy), was built between 1053 and 1080 beside an ancient longobardian church (Figure 1). In 1457, the original tower collapsed under a strong ground earthquake motion, and in 1499 a new tower was build next to the dome. The tower has a square cross-section in plan with 14m long sides. Its height is 45.5m. In the past, strengthening measures were adopted. As a way of confining the whole structure, horizontal tie bars were inserted at the 3rd and 4th floor level. An inspection of the tower was recently undertaken to evaluate its state of conservation. Some anomalies, such as biological colonisation,
surface deterioration, degradation of joints and cracks passing through the walls were observed. This situation, together with asymmetric restraints, suggested an investigation was lead to check the safety of the tower. The bell tower of Capua (Figure 2) was built in 861 during the Longobardian age. In 990 the original tower collapsed under strong earthquake ground motion, and it was rebuilt in the Norman age. The tower has a square cross-section in plan with sides 11.3m long. Its height is 41m. Limestone blocks from ancient buildings of Roman age form its basement, characterised by corner columns and double lancet windows. Its upper floors are made of clay bricks and campanian tuff. On the top of the bell tower four columns were erected to support a marble plate, but they were destroyed by the strong earthquake of 1457. In the past, laboratory and on-site investigations were carried out on the Bell Tower of Aversa: geometrical survey, survey of the crack patterns and of the deterioration distribution, chemical tests, monotonic compressive tests and, finally, single flat-jack tests in order to measure the stress state caused by the dead loads. In particular, monotonic compressive tests were carried out on 3 specimens taken from the base of the tower. The results are summarized in Table 1, where fcc is the compressive strength, Et is the tangent modulus of elasticity, Es is secant modulus of elasticity. The soil profile refers to two layers: the first one is composed by pyroclastic loose rocks; the second one is composed by Campanian ignimbrite. Focusing the attention on the soil that can interact with the structure, it is possible to recognize the homogenous groupings of Table 2. Also for the Bell Tower of Capua, the soil is mostly of volcanic origin and belongs to the pyroclastic sedimentary rocks group from the Phlegrean Fields (Table 3). Table 1. Results from compressive tests. Tower of Aversa No. 1 2 3
Description yellow tuff with grey pumices yellow tuff (lithoid facies) yellow tuff with grey pumices
fcc
Et
Es
4.23 3.99 3.82 2.85 3.66 1.92 3.46 1.92 2.08
Table 2. Soil profile under the bell tower of Aversa. No. Description 1 2 3 4 5
Thickness Depth (m) (m) Vegetable soil 3.00 0.00 Pyroclastic soil: ashes and pumices 1.70 3.00 Paleosoil 0.50 4.70 Pyroclastic soil: ashes and pumices 2.00 5.20 Campanian grey tuff bedrock 7.20
Figure 1. Dome bell tower of Aversa, Italy, XV century
Figure 2. Dome bell tower of Capua, Italy, XII century.
Table 3. Soil profile under the bell tower of Capua. No. Description 1 2 3 4 5
3
Vegetable soil Yellow Cinerite Brown Cinerite Brown tuff Campanian grey tuff
Thickness (m) 3.00 3.00 1.00 2.00 6.00
Depth (m) 0.00 3.00 6.00 7.00 9.00
EXPERIMENTAL DYNAMIC ANALYSIS
Ancient masonry buildings often have a high historical and monumental value and should be preserved. As a consequence, in this case the forced vibrations applied, for instance, by a mechanical vibrodyne, are not suitable for this use because even small vibrations are cannot be tolerated by these structures. On the contrary, measurement of environmental vibrations based on the natural noise and low frequency vibration from wind and traffic loading may be carried out without direct excitation of the building. In-situ experimental tests have been performed by applying Environmental Test Methods. These methods are relatively simple and, require equipment which is easily transported and can run even if the structure is in use. This technique, based on a careful choice of sensors positioning, has allowed obtaining natural frequencies and vibration modes from direct measurement. The response of the structure in the time domain has been recorded by a highly sensitive sensor network, integrated by a data acquisition system. The instrumentation used included: N.8 PCB piezoelectric accelerometers (Piezotronics model 393B04) (Fig.3); N. 1 data acquisition board (National Instruments DAQCard-16XE50); connector block for interfacing I/O (input/output) signals to plug-in data acquisition devices.
Figure 3. Accelometers used for vibration measurements
The accelerometers have been appropriately calibrated following the manufacturer's suggested procedures. For the Bell Tower of Aversa only wind and traffic vibrations have been monitored. The ambient vibration tests were carried out in April 2007. A preliminary numerical model was developed for selecting the location of the devices during vibration testing. The location of the accelerometers and the conditioners is shown in Fig.4. The measurements have been made within a 0÷6 Hz frequency range which is selected on the base of the first five natural frequencies of the tower obtained from the modal analysis of the preliminary numerical model. The spectral analysis of the recorded signals may give the natural frequencies and the corresponding mode shape. Usually, the signal recorded with this technique as well as the signal-to-noise ratio are very low. This implies that the recorded signal must be amplified and processed, and the negligible frequencies must be filtered through a 30 Hz low-pass filter. Data acquisition was driven by software written in Labview 8.0, which allows the acquisition of signals with sampling frequency of 100 Hz, and the real time visualization of accelerograms and Fourier spectra. The identification was performed using techniques of modal extraction in the frequency domain (Frequency Domain Decomposition - FDD). These techniques allow the assessment of natural frequencies and mode shapes. Fast Fourier transform (FFT) was used to determine the frequency spectrum of the signal.
Figure 4. Location of the sensors during environmental vibration measurement.
Often, a more useful alternative is Power Spectral Density (PSD), which describes how the power of the signal is distributed with frequency.The power spectral density (PSD) of the signals recorded by accelerometer 2 (X direction) and by accelerometer 3 (Y direction) are presented in Figures 5 and 6. The frequency-domain plot of power spectral density vs. frequency allows the peak picking and the identification of the natural frequencies of the Aversa Tower. For the Bell Tower of Capua not only the environmental vibrations, but also the motion of the tower subjected to the ringing of the bells were monitored on June 2008. The instruments consist of eight accelerometers (5 in Y-direction and 3 in X-direction) placed according to the measurement setup of Figure 7.
Figure 5. Power spectral density function - Accelerometer 2 Bell tower of Aversa.
Figure 6. Power spectral density function - Accelerometer 3 Bell tower of Aversa.
The spectral analysis of the recorded signals gives the natural frequencies and the corresponding mode shapes. Resonant frequencies are defined as clearly selected peaks on the spectra (Figures 8-10).
Figure 8. Power spectral density function -Accelerometer A Bell tower of Capua.
Figure 9. Power spectral density function -Accelerometer B Bell tower of Capua.
Figure 10.Power spectral density function -Accelerometer F Bell tower of Capua.
4
4.1
Figure 7. Location of the sensors during environmental vibration measurement. Bell tower of Capua.
VIBRATION-BASED PROCEDURE FOR STRUCTURAL IDENTIFICATION. Preliminary modelling
Environmental vibration measurement can provide more meaningful results if it is used to update a finite element model of the building. In this paper, an identification procedure based on the minimization of the error in frequencies, mode shapes and modal forces is proposed. First, a preliminary model was developed for selecting the location of the sensors during vibration testing. In particular, a detailed numerical model of the tower was developed and implemented with three-dimensional solid
elements using LUSAS FEA software. The structural geometry was obtained by carrying over a geometrical survey of the tower. In particular, the openings (doors, windows), the masonry floors (vaults), as well as the contribution of the foundation and surrounding soil have been considered in the analysis. The tower has been modelled using 8-node brick elements. A relatively large number of finite elements have been used in the model so that a regular distribution of masses could be obtained. The model results in a total of 3903 nodes and 2358 elements for the tower of Aversa, 47090 elements and 54066 nodes for the tower of Capua (Figs.11,12). The lateral arch connecting the Tower of Aversa with the Cathedral has been modelled with restraints in the direction parallel to the arch (Y-direction), while zero stiffness has been considered in the normal direction (Xdirection). During the calibration process of the numerical model, the values initially adopted were successively tuned. The uncertainty related to some parameters with major influence in the dynamic behaviour of the tower were considered, such as the localization and the elastic nature of supports, the Young’s and shear moduli of the walls.
The analyses were carried out in accordance with the hypothesis of linear elastic behaviour for masonry that is in the absence of significant tensile stresses during motion. Furthermore, the tower walls were assumed as homogeneous by taking an equivalent Young's modulus and an equivalent shear modulus. At first, the correction of the support conditions of the tower by trial-and-error was carried out until an acceptable likeness was obtained between the first five vibration mode shapes obtained from the FDD technique and given those by the numerical model. As ground characteristics are known, but the conservation condition of the foundation are lacking, it was decided to model the soil-structure interaction using linear elastic springs. For the tower of Aversa a normal stiffness of 0.50N/mm2 and a vertical stiffness of 2.0 N/mm2 were found. For the tower of Capua a normal stiffness of 0.9 N/mm2, a tangent stiffness of 0.6N/mm2 and a vertical stiffness of 2.0 N/mm2 were considered. The choice of the variation range is based on experimental values for analogous materials and on the results of monotonic compressive tests. In particular, for the tower of Aversa the range of the Young's modulus is 1600÷2000 MPa for the basement masonry and 2000÷3000 MPa for the body. For the tower of Capua the range Young's modulus range is 3400÷5800 MPa for the limestone basement and 1600÷4000 MPa for the clay bricks and Campanian tuff of upper levels. 4.2
Figure 11. Vibration mode shapes - Bell tower of Aversa.
Figure 12. Vibration mode shapes - Bell tower of Capua.
Calibration algorithm tuning the model
The calibration of the equivalent Young's modulus value assigned to the masonry walls of the tower was carried out by minimizing the error between frequencies numerical determined, mode shapes and modal lateral forces obtained numerically, and those resulting from the measurements performed on site. As expected the optimum value of Young's modulus is related to the parameter chosen for calibration. In the case the Bell Tower of Aversa, the number and location of the sensors during environmental vibration measurements are not satisfactory to give the mode shapes of the tower. As a consequence, mechanical parameters were defined minimizing the total frequency discrepancy. In particular, the frequency discrepancy Df=|fFEM-fFDD| between the frequencies from FEM model and FDD technique was evaluated. Then, the total frequency discrepancy is calculated with the following weighted mean:
Df
N i 1
f FEM ,i f FDD ,i i f FDD ,i
N i 1
i
(1)
wherei is the ith modal mass ratio and N is the number of the experimental mode shapes. A graphic representation of this analysis is shown in Figure 13 where the frequency discrepancy is plotted against the Young's modulus considered for the materials (Ebase for the limestone basement, Ebody for the upper levels). The surface is shown in an orthographic projection view. Kriging interpolation was used as the geostatistical gridding method to produce visually appealing contour and surface plots from irregularly spaced data. The minimum discrepancy Df=1.12% is obtained for Ebase=1700 MPa and Ebody=2250 MPa. In Table 4, the mechanical parameters tuning the finite element model to accurately reflect the dynamic characteristics of the Aversa Tower are reported. In Table 5 the comparison between the natural frequencies from dynamic identification and those from numerical modelling is reported.
Table 5. Numerical versus experimental frequency. Bell tower of Aversa. Mode type
fFDD (Hz) 1.05 1.37 4.81 4.89 5.05
1° flexural X 1° flexural Y 1° torsional 2° flexural X 2° flexural Y
fFEM (Hz) 1.06 1.36 3.76 4.64 6.14
DF (%) 0.95 0.73 21.8 5.11 17.7
The correlation between the measured and calculated modes reveals a good match, especially for 1st flexural X frequency (Df=0.95%) and 1st flexural Y frequency (Df=0.73%). In the case of the Bell Tower of Capua, combined frequency and mode shape data were obtained from dynamic investigations. As a consequence, it was possible to evaluate discrepancies in frequencies, mode shapes and modal force vectors. In general, the final aim of the dynamic investigations on these ancient masonry towers is the evaluation of their structural safety and seismic vulnerability. The calibration of the FEM model was therefore carried out to effectively simulate the modal force vectors of the tower. At first, the modal force vector discrepancy DF is estimated as follows: DF ,i
FFEM ,i FFDD ,i FFDD ,i
(2)
where FFEM,i and FFDD,i are the modal force vectors from numerical modelling and from dynamic testing, respectively, given by: FFEM ,i MFEM ,i FEM ,i Sa f FEM ,i FFDD ,i MFDD ,i FDD ,i Sa f FDD ,i
Figure 13. Frequency discrepancy plot against Ebody, Ebase. Bell tower of Aversa. Table 4. Optimized parameters. Bell tower of Aversa. Young’s modulus Poisson Mass density E (MPA) γ (Kg/m3) ratio Foundation 1800 0.15 1800 Basement 1710 0.15 1900 Body 2260 0.15 1600 Damaged lintels 2000 0.15 1800 Top 2000 0.15 1600 Masonry
(3)
where M is the mass matrix, Г is the modal participation factor, Sa is the spectral acceleration defined from the elastic demand response spectrum of the Italian Building Code (2008). The total modal force vector discrepancy is obtained by combining the discrepancies in the modal lateral forces in both directions, as follows:
D N
DF
F ,i
i 1
N
i 1
i
(4)
i
In Figure 14 the comparison between the modal force vectors FFEM,i and FFDD,i is reported. The modal force vector from numerical modelling has been referred to the Young's modulus values considered for the materials of
35
35
30
30
25
25
HEIGHT (m)
HEIGHT (m)
the Capua tower (3400÷5800 MPa for the limestone basement; 1600÷4000 MPa for the upper levels). The results have indicated that any variations in the elasticity modulus of the walls seem to have more influence on the 2nd flexural modal force pattern. In Figure 15 the modal force discrepancy defined by Equation 4 is plotted against the Young's modulus of masonry. The minimum value from grid statistics (DF=16.92%) is obtained for Ebase=5050 MPa and Ebody=1600 MPa. In Table 6 the mechanical parameters tuning the finite element model are reported. In Table 7 the natural frequencies from dynamic investigation are compared to the natural frequencies from numerical model. Also in this case a good correlation between measured and calculated frequencies was obtained, especially for the 1st flexural X (Df=1.59%) and the 1st flexural Y mode shape (Df=2.33%).
20 15 10
FDD method FEM model
5
20 15
10 FDD method 5 model FEM 0
0 0.00 0.05 0.10 0.15 0.20 0.25 0.30
Modal Force / Weight
-0.3
-0.2
-0.1
0.0
0.1
0.2
Modal Force / Weight
Figure 14. 1st flexural and 2nd flexural modal lateral force. Bell Tower of Capua.
Figure 15. Modal force discrepancy plot against Ebody, Ebase. Bell tower of Capua. Table 6. Optimized parameters. Bell tower of Capua. Masonry Foundation Basement Body
Young’s modulus Poisson Mass density E (MPA) γ (Kg/m3) ratio 2800 0.16 1600 5000 0.20 1800 1600 0.16 1600
Table 7. Numerical versus experimental frequency. Bell tower of Capua. Mode type 1° flexural X 1° flexural Y 1° torsional 2° flexural X 2° flexural Y
5
fFDD (Hz) 1.26 1.29 3.10 6.15 6.17
fFEM (Hz) 1.24 1.26 3.57 4.65 4.68
DF (%) 1.59 2.33 15.2 24.4 24.1
SEISMIC ASSESSMENT
The model after being updated and refined on the basis of the modal force tuning, was then used for the seismic assessment of the towers. At first, a static analysis was performed which take into account the presence of the dead load. The vertical stress map in the whole structure is depicted in Fig.16. The maximum compressive stress occurs at the bottom of the tower and has value of 1.32 MPa for the tower of Aversa and 1.04 MPa for the tower of Capua. These values are lower than the compressive strength of masonry. The seismic assessment was carried out by means of nonlinear static pushover analysis. Although the application of this analysis procedure has been introduced into seismic codes and Pre-standards (Italian Code (2008), Eurocode 8 (2004), ATC-40 (1997), FEMA-356 (2000), FEMA-440 (2005), ASCE/SEI 41-06 (2007)), several critical points were found when implemented to unreinforced masonry structures. In the case of masonry bell towers, the structure is regular in plan and elevation, but it has no rigid diaphragm. Furthermore, a distributed mass model rather than a lumped-mass model should be used for seismic assessment. Finally, a brittle damage mechanism generally occurs for masonry towers under lateral loads. As a consequence, the lateral load pattern is not modified during pushover as an effect of cracking, and so an invariable lateral load pattern may be used to reproduce the inertia forces deriving from earthquake ground motion. However, in the case of masonry towers, the higher-mode contributions become more significant. As a consequence, the combination of an important number of modes may be required to capture a satisfactory percentage of the total mass of the structure. An invariant and multimodal lateral load pattern was used for pushover analysis. In particular, the lateral load pattern F(x,y,z) is defined by the SRSS combination of the modal lateral force calculated from a response spectrum analysis including sufficient modes to capture at least 90% of the total building mass, as follows:
F x, y , z
x, y, z S T m x, y, z i
i
i
a
i
2
(5)
where i is the ith mode shape; i is the corresponding participation factor; m is the mass. The spectral acceleration Sa(Ti) is defined from the elastic horizontal ground acceleration response spectrum of the Italian Building Code (2008). The load was applied with increasing acceleration in horizontal direction. A control point at the top of the tower was considered in the analyses. The nonlinear constitutive model used for the masonry is based on classical cracking concrete with crushing material model. An exponentially decreasing tension softening was considered.
Figure 16. Vertical stresses due to dead load. a) Bell Tower of Aversa; b) Bell Tower of Capua.
the shear stress of the “explosion” effect of some blocks due to stress peaks. The region that is most sensitive to cracking is placed in the lower part of the tower. When the tensile strength of masonry is reached, the cracks start to open. The region that is most sensitive to crushing is the bottom part of the tower where the compressive stress is higher than the yield limit of masonry (Figs.16,17). As the amplification factor increases, the high stresses always appear at foundation level, due to the tensile stress between the foundation structure and the soil, until the structure collapses. A brittle damage mechanism in both towers therefore occurs. In Figure 18 the base shear is plotted against the calculated lateral displacement at the top of the tower. The displacement evolves almost linearly with base shear, due to the limited ductility capacity of the tower. However, damage in the structure increases, and when the total drift is greater than 0.150% for the Aversa tower and 0.269% for the Capua tower the ultimate compressive strength is reached. The capacity curve, which plots a force index (typically base shear V) against a deformation index (roof displacement TOP), may be modelled as straight linear (Fig.18). The seismic assessment was carried out with the capacity spectrum method based on inelastic demand spectra (Fajfar, 1999). Since the towers are distributed mass systems, the Capacity Spectrum in ADRS format (AccelerationDisplacement Response Spectra) may be obtained as follows:
x, y,z x, y,z dx dy dz V x, y,z x, y,z dx dy dz 2
Sa
Sd
Figure 17. Vertical stresses due to dead load and seismic load. a) Aversa’s Bell Tower; b) Capua’s Bell Tower.
The analysis evidences that the towers are basically in elastic conditions, since the level of stresses is smaller than the strength for all parts of the tower. The vulnerability analysis mainly consists in searching the potential collapse mechanism, in relation to the applied load. As long as the seismic action increases, some cracks appear at the top of the basement, mostly due to
2
TOP
x, y,zTOP
x, y,z x, y,z dx dy dz x, y,z x, y,z dx dy dz
(6)
2
(7)
where x,y,z) is the mass density and x,y,z) is the lateral displacement pattern. Since the pushover curve may be modelled as a straight line, the seismic demand is represented by means of 5%-damped Elastic Demand Response Spectra (EDRS) of the Italian Building Code. Consequently, the position of the performance point PP on capacity spectrum is defined by the intersection between the CS line and the 5%damped EDRS. In Figure 18, the comparison between EDRS and CS at the ultimate limit state is shown. The ultimate peak ground acceleration is PGAu=0.097g for the tower of Aversa and PGAu=0.196g for the tower of Capua.
SPECTRAL ACCELERATION (Sa/g) 0.20
0.30
0.500 0.400
REFERENCES
PP
0.300 0.200 0.100
PP 0.000 0.00
L./HEIGHT (%)
engineer who is asked to assess the seismic vulnerability of a structure and, eventually, what retrofitting is suitable.
0.600
2.00
4.00
6.00
8.00
10.00
SPECTRAL DISPLACEMENT Sd (cm)
Figure 18. Normalized capacity curve. b) Intersection between capacity and demand in ADRS format
The PGA for the structural collapse of the tower of Aversa is lower than the reference peak ground acceleration at the Life Safety Limit State (PGALS=0.169g), and so the risk index is LS= PGAu/PGALS=0.574. Instead, for the tower of Capua the ultimate peak ground acceleration (PGAu=0.196g) is greater than the peak ground acceleration at the Life Safety Limit State (PGALS=0.130g) and the risk index is LS=1.51. 6
CONCLUSIONS
The paper shows a methodology which can be applied to assess the seismic vulnerability of regular and tall masonry towers. The methodology can be synthesized as following: - Preliminary numerical model of the structure. - Environmental vibration test and elaboration of the recorded signal. - Dynamic identification of the structure and of the basic dynamic parameters. - Minimization of the error by mean of the weighted mean error in frequencies, according to different parameters for Young elastic modulus of the masonry and of the soil. - Perform nonlinear analysis (push-over) on the final identified model. The proposed vibration-based identification procedure provides a reliable tool to investigate the dynamic features of monuments when dealing with the uncertainties due to on the mechanical characteristic of the material. This approach seems effective in giving reliable results on mechanical properties of masonry structures, since most of the time the irregularities in the material cannot lead to a single value of elastic modulus valid all over the structure. The increasing diffusion of dynamic tests, even performed under environmental vibrations, will give more confidence to the
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