We examine an application of Acoustic Emission (AE) technique for a probabilistic analysis in time and space of earthquakes, in order to preserve the valuable Italian Renaissance Architectural Complex named “The Sacred Mountain of Varallo.” Among the forty-five chapels of the Renaissance Complex, the structure of the Chapel XVII is of particular concern due to its uncertain structural condition and due to the level of stress caused by the regional seismicity. Therefore, lifetime assessment, taking into account the evolution of damage phenomena, is necessary to preserve the reliability and safety of this masterpiece of cultural heritage. A continuous AE monitoring was performed to assess the structural behavior of the Chapel. During the monitoring period, a correlation between peaks of AE activity in the masonry of the “Sacred Mountain of Varallo” and regional seismicity was found. Although the two phenomena take place on very different scales, the AE in materials and the earthquakes in Earth’s crust, belong to the same class of invariance. In addition, an accurate finite element model, performed with DIANA finite element code, is presented to describe the dynamic behavior of Chapel XVII structure, confirming visual and instrumental inspections of regional seismic effects.
The Sacred Mountain of Varallo is located in the Italian province of Vercelli. Built on a cliff above the town of Varallo, it is the oldest and most important Sacred Mountain of the Alps (Figure
The Sacred Mountain of Varallo, Italy. Overview.
Its story began in the late fifteenth century when the Franciscan friar Bernardino Caimi of Milan, returning from the Holy Land where he was guardian of the Holy Sepulchre, decided to reproduce in Varallo the holy places of Palestine [
The “New Jerusalem,” as it was called the Sacred Mountain, initially intended to represent the distant sites of the Christian tradition for all those people who could never go there (Figure
The Sacred Mountain of Varallo. The Square of Tribunals.
Chapel XXXIII.
The Acoustic Emission monitoring was conducted on the frescoed masonry walls of the Chapel XVII of the Sacred Mountain of Varallo: the Chapel of the Transfiguration of Christ on Mount Tabor (Figure
Chapel XVII.
One of the purposes of monitoring by means of AE sensors applied to the frescoed wall was to detect the AE signals from a region of the wall in which the frescos show a plaster detachment. Moreover, we used the collected data coming from the “in situ” monitoring in order to assess the seismic risk of artworks and possible collapses due to earthquake actions [
As regards the structural integrity, the North wall of the Chapel XVII shows a vertical crack of about 3.00 m in length and a detachment of frescos. These phenomena were one of the objective of the monitoring campaign by means of AE technique. Six AE sensors were employed to monitor the damage evolution of the structural support of the decorated surfaces: four were placed around the vertical crack while two were positioned near the frescos detachment (Figure
Chapel XVII. View of the monitored areas. Left side: sensors 5, 6, and the frescos detachment. Right side: sensors 1–4 and the vertical crack.
For the sensor pasting on decorated surfaces, a suitable methodology was applied. The necessary operations for bonding the AE sensors to the wall were carried out by a group of restorers, which have prepared a film of Japanese paper, on the surface of which is coated a thin layer of “Paraloid.”
The “Paraloid” is an acrylic resin (methyl acrylate soluble in ketones, esters, hydrocarbons, and chlorinated hydrocarbons) and is used in the field of restoration as a consolidant at low concentrations (2,4%) or as an adhesive at higher concentrations. It allows an excellent waterproof performance and has the advantage of being reversible and long-term stable. The layer of “Paraloid” forms a good protective base for the AE sensors bonding with silicone glue. The sensors were applied to monitor both the vertical crack and the detachment of the plaster (Figure
The Acoustic Emission acquisition system is shown schematically in Figure
AE acquisition system.
The monitoring time started from May 9, 2011, and finished on September 5, 2011. Regarding the monitoring results on the chapel structural integrity, they are reported in [
Nondestructive testing methods are currently used to evaluate structural damage phenomena and to predict their development over time. It is worth noting that the evaluation of damage in historic buildings is often a complex task. It is essential to distinguish between stable damage patterns and damage in evolution towards a catastrophic collapse. Some structural damage can be triggered by events such as earthquakes. Furthermore, the limited ductility of the masonry, combined with the large size of this type of construction, provides a rather fragile structural behavior. Fortunately, the damage evolution in time can be effectively evaluated by means of the AE technique [
Moreover, the statistical distribution of earthquakes shows a complex nonlinear space-time behavior, that reflects the heterogeneities of the Earth's crust. Despite this complexity, a scaling law is universally valid: the earthquakes frequency-magnitude statistical distribution provided by the Gutenberg-Richter (GR) law [
On the other hand, AE in materials and earthquakes in the crust are very similar from many aspects and correlated in time, even though they occur at very different scales [
Most earthquakes have precursors, that are phenomena that in the short or long term change their activity before the earthquake. In the literature, many precursors have been proposed, but there is still no clear evidence about their reliability. In addition, any operative warning procedure must be based on the acquisition of a combination of several precursor clues. Recently, major efforts in the field of earthquake prediction have focused on the fluctuations of the physical parameters of the crustal rocks of the seismically active continental areas, and on regular intervals in the space-time distribution of earthquakes [
When a crack in the Earth's crust increases (i.e., a fault propagate), the corresponding AE show, progressively lower frequencies, eventually decreasing from the ultrasound field down to the sonic range: as it occurs during the well-known phenomenon of seismic roar. Thus, AE techniques can be effectively put into relation with the spread of tensions through the Earth’s crust. Some Italian researchers collected continuously, for many years, the AE signals from below the Gran Sasso massif [
Among the various studies on the earthquakes space-time correlation, there is a statistical method that allows to calculate the degree of correlation both in space and time between a series of AE and the local seismic recordings, collected in the same period. This analysis is based on the generalization of the space-time correlation known as the integral of Grassberger-Procaccia [
Therefore, between all possible pairs of recorded AE and seismic events, the sum expressed by the integral of Grassberger-Procaccia can be calculated for those having the epicentral distance
Note that, in order to evaluate (
Anyway, this approach does not consider the chronological order of the two types of events. Since the AE time series and the earthquake sequences are closely intertwined in the time domain, the problem of the predictive ability of the AE peaks is still open. The records of AE could be both the consequences of the progressive development of microdamage or the effect of widespread microseismicity. Therefore, a probabilistic analysis can be carried out discriminating between the AE events prior to the earthquake, which are precursors, and the AE following the earthquake, which are aftershocks. This analysis can be performed adopting a modified correlation integral [
In this way, the function
AE as precursor from May 9, 2011 to June 16, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0339 | 0.1121 | 0.2018 |
2 weeks | 0.0772 | 0.2130 | 0.3661 |
3 weeks | 0.1228 | 0.3018 | 0.4875 |
4 weeks | 0.1487 | 0.3661 | 0.5549 |
5 weeks | 0.1630 | 0.4321 | 0.6210 |
AE as aftershock from May 9, 2011 to June 16, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0254 | 0.0732 | 0.1437 |
2 weeks | 0.0357 | 0.1196 | 0.2629 |
3 weeks | 0.0371 | 0.1509 | 0.3362 |
4 weeks | 0.0371 | 0.1652 | 0.3732 |
5 weeks | 0.0371 | 0.1665 | 0.3768 |
AE as precursor from July 5, 2011 to September 5, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0075 | 0.0278 | 0.0846 |
2 weeks | 0.0184 | 0.0552 | 0.1896 |
3 weeks | 0.0239 | 0.0833 | 0.3222 |
4 weeks | 0.0346 | 0.1040 | 0.3841 |
5 weeks | 0.0498 | 0.1210 | 0.4435 |
6 weeks | 0.0557 | 0.1268 | 0.5130 |
7 weeks | 0.0557 | 0.1268 | 0.5497 |
8 weeks | 0.0557 | 0.1268 | 0.5607 |
9 weeks | 0.0557 | 0.1268 | 0.5657 |
AE as aftershocks from July 5, 2011 to September 5, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0045 | 0.0298 | 0.1192 |
2 weeks | 0.0132 | 0.0465 | 0.1916 |
3 weeks | 0.0234 | 0.0717 | 0.2592 |
4 weeks | 0.0301 | 0.0970 | 0.3251 |
5 weeks | 0.0313 | 0.1114 | 0.3737 |
6 weeks | 0.0313 | 0.1246 | 0.4164 |
7 weeks | 0.0313 | 0.1299 | 0.4283 |
8 weeks | 0.0313 | 0.1336 | 0.4333 |
9 weeks | 0.0313 | 0.1341 | 0.4338 |
Filtered AE as precursor from July 5, 2011 to September 5, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0080 | 0.0290 | 0.0829 |
2 weeks | 0.0197 | 0.0592 | 0.1969 |
3 weeks | 0.0252 | 0.0866 | 0.3288 |
4 weeks | 0.0364 | 0.1081 | 0.3920 |
5 weeks | 0.0517 | 0.1248 | 0.4538 |
6 weeks | 0.0577 | 0.1308 | 0.5267 |
7 weeks | 0.0577 | 0.1308 | 0.5625 |
8 weeks | 0.0577 | 0.1308 | 0.5731 |
9 weeks | 0.0577 | 0.1308 | 0.5776 |
Filtered AE as aftershocks from July 5, 2011 to September 5, 2011. Cumulative probability
60 km | 80 km | 100 km | |
---|---|---|---|
1 week | 0.0042 | 0.0294 | 0.1149 |
2 weeks | 0.0117 | 0.0464 | 0.1889 |
3 weeks | 0.0203 | 0.0681 | 0.2521 |
4 weeks | 0.0278 | 0.0935 | 0.3142 |
5 weeks | 0.0292 | 0.1074 | 0.3604 |
6 weeks | 0.0292 | 0.1202 | 0.4041 |
7 weeks | 0.0292 | 0.1253 | 0.4151 |
8 weeks | 0.0292 | 0.1292 | 0.4213 |
9 weeks | 0.0292 | 0.1297 | 0.4218 |
Evolution of the modified correlation integral for different time windows, during the two monitoring period. (a) Monitoring time from May 9, 2011 to June 16, 2011, see Tables
For this analysis, the AE collected data are grouped into two different time windows. The first time window started May 9, 2011, and finished June 16, 2011. The second time window started July 5, 2011, and finished September 5, 2011. Both time windows involved the monitoring of the vertical crack and of the frescos detachment [
In this section, we obtain a correlation between seismic and acoustic events through the application of the modified integral of Grassberger-Procaccia.
The data series of analyzed AE are shown in Figures
Seismic events around Varallo (Italy) from May, 2011 to September, 2011 (LM: local magnitude).
Sacred Mountain of Varallo: cumulated AE and seismic events from May 9, 2011 to June 16, 2011 (LM: local magnitude).
Looking at the temporal distribution of earthquakes in relation to the cumulative AE trend, a quite good correspondence between AE peaks and earthquake events can be observed (Figures
Sacred Mountain of Varallo: cumulated AE and seismic events from July 5, 2011 to September 5, 2011 (LM: local magnitude).
The probability values obtained for the period May-June show that, regardless of the distance and of the correlation time, the probability of a seismic event following a peak of Acoustic Emission (AE
It is interesting to note that, for both monitoring periods, within a radius of 60 km from the monitored site, the AE signals still play their role as seismic precursors, as it can be assessed observing the values of the cumulative probability
More in detail, within a radius of 60 km, there is a clear tendency of AE signals to anticipate earthquakes, and behave as precursors. At a distance of 80 km, AE are precursor signals only in the time window comprised between 2 and 6 weeks, were
In any case, it is worth distinguishing between the environmental contributions due to crustal trembling (external source), and the structural damage contributions (inner source) to AE activity on the Chapel XVII.
To better analyze the results from the second monitoring period (Tables
The results are shown in Tables
The Chapel XVII was discretized with three-dimensional linear pyramid elements, accounting for the accurate geometry of the stone masonry structure. The shapes of the cylindrical chapel and of the above spherical dome are precisely discretized, taking into account the various apertures, the inside internal vault supporting the Mount Tabor installation, and the outside pronao with columns. On the contrary, the wooden roof structure was considered only as an external load. The mesh of the structure is shown in Figure
Finite element mesh of Chapel XVII: half of the model.
Elastic response spectrum of acceleration
The dynamic analysis, performed with the commercial finite element code DIANA [
Natural frequencies of the first 20 calculated modes of vibration of Chapel XVII and percentages of mass involved in each mode of vibration for directions
Mode | Frequency (Hz) | Period (s) |
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% | Cumulated% | % | Cumulated% | |||
1 | 4.737 | 0.211 |
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2 | 5.162 | 0.194 |
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3 | 8.570 | 0.117 |
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4 | 9.891 | 0.101 |
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5 | 10.087 | 0.099 |
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6 | 13.192 | 0.076 |
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7 | 13.373 | 0.075 |
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8 | 13.881 | 0.072 |
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9 | 14.479 | 0.069 |
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10 | 14.616 | 0.068 |
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11 | 15.633 | 0.064 |
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12 | 17.402 | 0.057 |
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13 | 17.612 | 0.057 |
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14 | 18.031 | 0.055 |
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15 | 18.677 | 0.054 |
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16 | 18.750 | 0.053 |
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17 | 19.165 | 0.052 |
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18 | 19.874 | 0.050 |
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19 | 20.545 | 0.049 |
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20 | 21.578 | 0.046 |
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Chapel XVII mode 1 of vibration (a); Chapel XVII mode 2 of vibration (b); Chapel XVII mode 3 of vibration (c).
Figure
Chapel XVII principal SRSS stress contour, measured in Pa, during simulated earthquake in the
Chapel XVII deformed shape.
The FEM analysis provides stress levels under dead loads near to the vertical cracks that are not so high for a stone masonry with mortar joints (see Figures
A more detailed mechanical characterization of the masonry is currently under development to perform the subsequent nonlinear analysis.
Besides the canonical use in nondestructive tests, the heuristic potential of AE monitoring of civil structures for earthquakes prediction appears very intriguing. Starting from the assumption that any structure should not be regarded as separated from its environment, a method of correlating AE activity on the Renaissance Complex of the Sacred Mountain of Varallo subjected to a long-term monitoring with regional seismicity is investigated. Two qualitatively very similar phenomena such as Acoustic Emission and earthquakes become two aspects of a unique phenomenon, which looks self-similar.
Furthermore, in this work, by applying the modified Grassberger-Procaccia correlation algorithm, with the aim of explaining the correlation between regional seismicity and Acoustic Emission emerging from the Chapel XVII of the Sacred Mountain of Varallo, it is observed that the structure behaves as sensitive receptors for earthquakes occurring within a radius of about 100 km, distinguishing environmental contributions to AE activity on the Chapel XVII due to crustal trembling (external source) from contributions due to structural damage (inner source). An accurate finite element model, performed with DIANA finite element code for the dynamic analysis of Chapel XVII structure, is utilized to confirm visual inspections and monitoring the results of the earthquakes’ effects.
The financial support that is provided by the Piedmont Region (Italy) to the Project “