Foreword

1.1 Historical notes and description

The "Scaligeri" or "della Scala" family was a dynasty that ruled Verona, in Italy, for over a century, from 1262 to 1387. Cansignorio della Scala (1340-1375) managed the city in a relatively peaceful period, and adorned Verona in a way to make it call "marmorina" (marbled) for the abundant use of ancient marbles and roman statues.

The stone tomb of Cansignorio della Scala was built between 1374 and 1376, by will of the same Cansignorio, when he was still alive. The tomb was erected close by the St. Maria Antica church, where the tombs of Cangrande and Mastino the 2nd (his grandfather and father respectively) were already built by local workers. Differing from his ancestors, Cansignorio desired a monumental tomb, where the architectural aspect was more important than the decorative. The work was then commissioned to Bonino da Campione, a famous master of gothic sculpture. The monument, based on a hexagonal plan, is adorned with sculptures and spired tabernacles, with the overhanging equestrian statue of Cansignorio. The tomb is surrounded by an hexagonal wrought iron fence, at whose corners rise six pillars

Figure 1. The stone tomb of Cansignorio (on the right) and Mastino the 2nd (rear left), near the St. Maria Antica church.
Figure 2. The upper part of the Cansignorio stone tomb: below the gablets with the statues of the virtues and the tabernacles with angels; above the equestrian statue.

sustaining gothic tabernacles, containing statues of the saint-warriors (St. George, St. Martin, St. Quirinus, St. Sigismund, St. Valentine and St. Louis, king of France). The tomb starts with six columns sustaining a red marble slab on which finds place the white marble sarcophagus, sustained by eight pillars and decorated with bas-reliefs representing Gospel scenes. The cover of the sarcophagus hosts a lying statue of Cansignorio, watched over by angels.

At the second level, six further spiral columns sustain the canopy with polylobed arches. Above these finds place a cornice sustaining six gablets with allegorical figures representing the virtues. At the corners are positioned six further tabernacles with statues of angels. The roof, corresponding to an hexagonal pyramid made of white marble, finally supports the massive equestrian statue of Cansignorio

The stones used for the erection of the tomb are the "Candoglia" white marble, the same employed in the Milan's cathedral, and the "Rosso di Verona" (Verona's red marble), besides the Pietra Gallina (a soft limestone from Vicenza). The inner part of the roof (above the crossed vault and behind the stone facing of the canopy) is composed by solid brickwork masonry.

1.2 Past restoration works

Throughout the centuries, several repair interventions were necessary to preserve the delicate structure of the stone tomb, such as those carried out in the XVII, XIX and XX centuries. In 1676 the Verona municipality adopted a resolution to execute restoration works on the tomb, comporting strengthening interventions and substitutions on the upper part ofthe monument, without however intervening on the supporting elements. Between 1827 and 1829 other restoration works were carried out, raising arguments on the type of marble to be used in substitutions of the deteriorated parts. Between 1838 and 1844 the fence was restored, and on the 24th of July 1840 a portion of the southern gablet fell down, being subsequently restored (1846) and lodged back in the original position. Substitutions comported the use of Candoglia marble elements, secured with iron clamps fixed with melted lead. The sealing of the cracks was performed with filler. Main interventions carried out were: the reconstruction of the spires of some tabernacles; the positioning of steel reinforcing elements on two columns of a tabernacle; the complete reconstruction of a column and capital of a tabernacle, and of some gablets between the spires; the reconstruction of the tail and the left rear leg of the horse in the equestrian statue; the substitution of the copper tie beams of the tabernacles with saint-warriors with new ones in iron; the sealing of the vault's groins.

Other interventions, similar to those executed at the half of the XIX century, were carried out between 1910 and 1914. The monument was then protected against bombing during the two world wars. In 1919, after the removal of the shields, some light restorations were carried out. Then, during the positioning of the shields of the 2nd world war, an analysis of the conditions of the tombs was carried out, with successive light restoration works.

2 THE INVESTIGATION ACTIVITIES 2.1 Dynamic identification

Between different Non Destructive techniques that may be profitably used for the achievement of an advanced knowledge of the structural layout of a historic masonry building, dynamic identification proved to be a very effective tool (Modena et al., 2001; Gentile et al., 2004; Ramos et al., 2006), being actually the only method able to experimentally define parameters related to the global structural behavior. Prior to the installation of a Structural Health Monitoring (SHM) System, a dynamic investigation campaign took place in August 2006. Tests were aimed at the definition of the optimal SHM system sensors' positioning, and at the characterization of the dynamic properties of the monument for FE modelling calibration purposes.

Figure 3. Identified mode shapes: (a) 1st bending N-S, 3.19 Hz; (b) 1st bending E-W, 3.24 Hz; (c) 1st torsion, 5.88 Hz; (d) 2nd bending N-S, 12.55 Hz; (e) 2nd bending E-W, 12.88 Hz; (f) 2nd torsion, 19.42 Hz; (g) FDD method, average of the normalized singular values of spectral density matrices of all test setups.

Figure 3. Identified mode shapes: (a) 1st bending N-S, 3.19 Hz; (b) 1st bending E-W, 3.24 Hz; (c) 1st torsion, 5.88 Hz; (d) 2nd bending N-S, 12.55 Hz; (e) 2nd bending E-W, 12.88 Hz; (f) 2nd torsion, 19.42 Hz; (g) FDD method, average of the normalized singular values of spectral density matrices of all test setups.

Following the mode shapes emerged from the FE numerical model, sensors were placed at the first level (in the stone slab where the sarcophagus stands), at the second level (on the cornice above the pointed arches) and at the top of the monument (at the foot of the equestrian statue). A total of six sensors was employed, considering three test setups for a total of 6 acquisition points, recording the acceleration in orthogonal (and parallel to the ground) directions.

The acquisition system was composed by a compact unit provided with 24-bit digital acquisition cards, connected to piezoelectric mono axial acceleration transducers. Once fixed the transducers to the structure in the selected positions, tests consisted in acquiring data over a predetermined period, at a determinate sample rate. Each test setup consisted in recording the signal two times (65,536 points each) whit a sampling frequency of 100 SPS (samples per second), with an overall setup signal recording duration of 21 '51^. For the identification of the modal parameters (natural frequencies and corresponding mode shapes), output only identification techniques were used (Operational Modal Analysis). In particular, the recorded ambient vibrations were related to the wind excitation and urban traffic.

The modal parameter extraction method selected was the FDD - Frequency Domain Decomposition -technique (Brincker et al. 2000) which estimates the modes, with the assumption that the excitation is reasonably random in time and in the physical space of the structure, using a Singular Value Decomposition (SVD) of each of the spectral density matrices. The data series acquired at 100 SPS were processed by a decimation of 2 (Nyquist frequency of 25 Hz), with segment length of 2048 points and 66.67% window overlap. Several peaks related to structural frequencies were detected in the frequency domain and the corresponding mode shapes defined (Fig. 3).

2.2 Monitoring

The Structural Health Monitoring System (installed in December 2006) is aimed at the control of static

Figure 4. Positioning of the acceleration (left) and displacement sensors (right).

and dynamic parameters related to the structural functioning of the monument. The system is composed by an acquisition unit connected to six piezoelectric accelerometers, two potentiometric displacement transducers and a temperature and relative humidity sensor. The central unit, located at the base of the tomb, is provided with a WiFi router for remote data transmission.

The monitoring strategy is conceived both to collect data at predetermined time-intervals (periodic monitoring, i.e. cracks opening, changes in the dynamic response) and to automatically start to save data in case of significant external events (such as seismic events). Such controls will permit to appreciate possible variations in the assessed structural functioning with the passing of time and to have a record of the dynamic behavior of the stone tomb during severe events.

The acceleration transducers are placed in suitable positions in relation to the mode shapes of the structure, as shown by the numerical modeling/dynamic identification (Fig. 4, left). Four sensors are placed on two levels for the evaluation of the vibration in the NS and EW direction (bending modes) and in the horizontal planes (torsion modes).

A couple of reference sensors is fixed at the base for the record of the ground acceleration both in operational conditions (i.e. evaluation of the traffic induced vibrations) and during seismic events. A temperature/relative humidity sensor is fixed at the intrados of the marble slab (first level). The displacement transducers are positioned across significant cracks (Fig. 4, right, see also Fig. 14). The temperature, relative humidity and displacement of the selected points (crack mouth opening) are recorded each 6 hours, corresponding to 4 daily readings. Dynamic data are collected both at fixed time intervals (each 48 hours, approximately 22' of recording at a sample rate of 100 Hz) and on a trigger basis (shorter records, signals are recorded when the vibration exceeds a predefined threshold).

No meaningful variations in terms ofdisplacements were reported up to November 2007 (Fig. 5a). Variations remain limited and related to the environmental parameters, presenting maximum differences (corresponding to crack mouth opening) of about 1/10th of millimeter. No seismic events were recorded in the monitored period. Limited shifts (max 4%) were noted in all of the identified frequencies (see also Ramos et al., 2007), possibly related to environmental parameters, as reported in Figures 5b and c (slight decrease with the relative humidity, seasonal variations).

3 STRUCTURAL MODELS 3.1 Introduction

A detailed FE numerical model, based on a laser scanner geometrical survey of the monument previously carried out, was implemented in order to evaluate the static and dynamic behaviour of the monument. The evaluation of the initial results of the numerical model (linear static and natural frequency analyses) assisted the design phase of the strengthening intervention and indicated the most suitable places for the sensors' positioning (dynamic identification and monitoring). The first model was calibrated on the basis of the results of the experimental activities, in order to be subsequently used to simulate the response of the monument to different external actions.

3.2 The FE model

As a first step, linear elastic constitutive laws were assigned to all materials in order to define the static load pattern (self weight) and the dynamic properties of the monument. The model is composed by approximately 49,000 brick elements and 53,600 nodes. Finite elements' sides are comprised between 0.10-0.15 m. The mesh is more refined in the slender elements (columns) and in the junctions, rougher elsewhere. The decorative elements and statues were modelled as the structural parts: only areas too small to be considered significant were neglected (Fig. 6).

The linear static analysis (self weight) indicates that compressive stresses reach their maximum values in the columns, where stresses of about 1.0-1.5 MPa (lower order) are found. In small areas of the upper order of columns compressive stress peaks of 2.0 MPa are noted. Tensile stresses generally present very low values or close to zero. However, non negligible tensile

Figure 5. Monitoring results: (a) displacement transducers PZ1/PZ2 and environmental parameters, recorded data plotted vs. time; dynamic parameters, identified frequencies: (b) first two bending frequencies vs. time and (c) vs. relative humidity.

Figure 6. (a) Rendered view of the FE model, East side; (b) corresponding mesh. The positive Y axis corresponds to the North direction.

Table 1. Experimental vs. numerical frequencies.

Frequency (Hz)

Table 1. Experimental vs. numerical frequencies.

Frequency (Hz)

Mode

Description

Exp.

FE model

diff. %

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