Time Series Analysis of Acoustic Emissions in the Asinelli Tower during Local Seismic Activity

Abstract

The existence of ongoing damage processes in a masonry wall of the Asinelli Tower in Bologna have been investigated by the acoustic emission (AE) technique. A time correlation between the AE activity in the monitored structural element and the nearby earthquakes has been observed. In particular, the largest cluster of AE signals has been recorded within a few hours after the main shock (4.1 magnitude) occurrence. The presented findings suggest that aging and deterioration of the monitored structural element significantly depend on the action of light earthquakes, even at considerable distance. Trends of two evolutionary parameters, the b-value and the natural time variance κ₁, have been derived from the AE time series in order to identify the approach of the monitored structural element to a “critical state” in relation to the earthquake occurrence.

1. Introduction

Fracture precursors in metallic [1,2] and quasi-brittle materials like rocks [3,4], concrete [5,6,7,8,9], and masonry [10,11] can be experimentally investigated focusing on the statistical properties of an acoustic emission (AE) time series from growing micro-fractures, where the discovery of underlying scaling laws suggests a description of fracture as a critical phenomenon [12,13,14,15,16,17,18,19,20,21]. Within this context, finding fracture precursors means identifying critical scaling exponents and early indicators of the approach to a critical state [22].

The relevance of the AE applications in civil engineering for structural health monitoring is widely recognized. In this regard, it is increasingly necessary to give the highest priority to seismic risk mitigation in large portions of the Italian territory. Minor and light earthquakes can drive invisible damage processes in buildings and monuments, which eventually result in catastrophic collapses during stronger earthquakes. It is worth noting that AE can be exploited as a diagnostic tool in geophysics as well, since recent experimental evidences and theoretical studies support the hypothesis that increased AE and electromagnetic activities may be signature of crustal stresses redistribution in a large zone during the preparation of a seismic event [23,24,25,26,27,28,29,30,31,32,33,34]. Laboratory studies have been motivated by the need to provide tools for the earthquake prediction [35].

Therefore, the AE structural monitoring might potentially provide twofold information: one concerning the structural damage and the other concerning widespread micro-seismic activity, propagating across the ground-building foundation interface, for which the building foundation represents a sort of extended underground probe [10,11,21,23,24,30,33].

The presented research study was initially motivated by the debate about the alleged incompatibility between heavy vehicle traffic and Bologna’s historical center, which concerns also the structural stability of two medieval towers, the Garisenda and the Asinelli (the taller) [36]. As reported in a previous publication [30], the influence of environmental phenomena on the AE activity in the Asinelli tower, such as the flux of surrounding vehicle traffic, unusual anthropogenic activities, and wind action, has been excluded. Actually, the nearby seismicity apparently has some influence on the AE activity detected in a masonry wall of the tower [30]. Here, the focus is on the time correlation observed between the largest AE cluster and the strongest (magnitude 4.1) local earthquake, with an epicenter 100 km far from the monitoring site.

2. Materials and Methods

An array of six broadband AE transducers (with a flat frequency response nominally in the range of 50–500 kHz, as declared by the manufacturer, i.e., well beyond the frequency range of signals propagating in the masonry) was fixed to the north-east angle of the Asinelli Tower at an average height of 9.00 m above ground level. The frequencies of interest in the old masonry, around 30 kHz, were still detected by the adopted transducers as already reported in previous papers for similar surveys [37]. Figure 1a–c show the tower and the transducers applied to a masonry wall portion.

The transducers were connected to a six-channel acquisition system able to store AE signal parameters such as arrival time t (determined with accuracy of 0.2 μs), duration, peak amplitude, and ring-down count (number of times the AE signal exceeds a preset threshold). A time accuracy of 0.2 μs, equivalent to a sampling rate of five mega-samples per second, is adequate to measure frequency components up to 500 kHz (only frequencies up to 10 times smaller than the sampling rate are usually considered), covering satisfactorily the AE frequency range.

Prior to starting the monitoring, were preliminarily performed for a representative period of time, i.e., 8 h, in order to determine the level of spurious signals. Thus, the signal acquisition threshold was set to 100 μV in order to filter out the electrical noise (see a typical signal waveform in Figure 1d). Keeping fixed the threshold made it possible to capture possible variations in the noise level due to changeable environmental conditions like traffic, weekdays, weekends, etc.

AE monitoring began on 23 September 2010 at 5:40 p.m. and ended on 28 January 2011 at 1:00 p.m. for a 2915-h period [30]. All the AE signals were found to fall in the amplitude range of 100 to 12,800 μV or, equivalently, of 40 to 82 dB, if the signal peak amplitudes $A_{\max }$ are expressed in decibels (dB), $A_{\mathrm{dB}}=20{\log }_{10}\left(A_{\max }/1\mathsf{\mu }\mathrm{V}\right)$ [38]. Because of heterogeneity of masonry, the point location method of AE sources exploiting signals recorded by multiple transducers could hardly be applied.

3. Results

3.1. Correlation between AE and Earthquakes

The plot of the AE signals count rate over the monitoring time (Figure 2) suggests that the masonry wall is undergoing a damage process. The clusters of AE hits, especially around the time 500 h, can be regarded as signature of high crack growth rate. During the monitoring period, frequent seismic events occurred in the region [30], but only those that might have affected the stability of the tower have been considered. Basing on their magnitude and epicentral distance, we have selected the two strongest regional earthquakes (the magnitude 4.1 event that hit the Rimini area on 13 October 2010 at 11:43 p.m. with epicenter about 100 km far from Bologna, as shown in Figure 3, and the magnitude 3.4 event recorded in the Modena Apennines on 21 November 2010 at 4:10 p.m.) and the nearby earthquakes with magnitude ≥0.5 and epicentral distance ≤20 km from the monitoring site.

Figure 2a shows the AE signals count rate and the earthquake time series, referring to the entire monitoring period, where a correlation in time between AE clusters and seismic events can be observed. A significant example is given by the seismic and the AE sequences that occurred between 1500 and 1800 h. Even more remarkably, the densest AE cluster (formed by 4000 hits and highlighted by the dashed frame in Figure 2) and the magnitude 4.1 earthquake that occurred on 13 October 2010 at 11:43 p.m. appear to be closely correlated.

Unless uncontrolled factors affecting the measurements, the main seismic shock apparently triggered temporary intensification of the AE activity, revealing local instability until the recovery of equilibrium. The comparatively longer duration of this AE cluster with respect the earthquake duration could be explained by a viscoelastic behavior, assumed for masonry structures [39], which would produce stress and strain over time in response to an impulsive load [40].

3.2. b-Value versus Natural Time Analyses of AE Time Series

In order to investigate the entrance of the structural element to a critical state, we focus on the cluster of AE hits occurred in the interval 490–510 h. The temporal evolution of two AE parameters has been considered: the b-value of the Gutenberg-Richter (GR) law, and the variance κ₁ of the natural-time transformed time series [25,26,27].

The GR law, initially introduced in seismology [41] and then extended to the statistics of AE signals [38,42,43,44,45,46], is expressed by the relation

$${\log }_{10}N=a-b\times M$$

(1)

where $M\equiv {\log }_{10}\left(A_{\max }/1\mathsf{\mu }\mathrm{V}\right)$ is the magnitude [38,45], i.e., the logarithm of the AE peak amplitude, N is the incremental frequency, i.e., the number of AE hits with magnitude greater than the threshold M, and a and b (termed as b-value) are empirical constants to be fitted. The standard error of b-value is $b/\sqrt{N}$ for a population of N samples and 95% confidence limits are twice this value.

The b-value is the negative slope of the linear descending branch of the GR law, and it grossly represents the relative number of micro-fractures to macro-fractures. Generally, systematic decreasing b-values are indeed observed during laboratory loading tests, with a single minimum just prior to specimen failure [38,42,43,44,45,46].

In the present study, the b-value analysis has been carried out twice, by partitioning the data set in groups formed by 300 and 800 hits. The b-value of each subset has been obtained through Equation (1) and regression analysis in the linear range of GR graphs, from 2.0 to 3.8 or 4.1 magnitude (i.e., from 40 to 76 or 82 dB). The related time series of b-values exhibit similar trends, especially sharing a global minimum b = 0.9–1 at time t_b-min = 501 h (marked in bottom diagram of Figure 4). It is worth remembering that b-values close to unity correspond to the growth of macro-fractures in the monitored element [38,39].

The results of the b-value analysis appear to be reliable, as they are substantially independent from the chosen partition. The final trend toward higher b-values suggests that the monitored masonry wall is substantially stable, with a damaging episode driven by the specific seismic event, and interpretable as a sign of enhanced structural sensitivity to light earthquakes.

In order to take into account variations in the statistical properties of the AE amplitude distributions, the “improved b-value” (Ib) was introduced and defined as follows [42,44,45]:

$$Ib=\left[{\log }_{10}N\left(\mu -{\alpha }_1\sigma \right)-{\log }_{10}N\left(\mu +{\alpha }_2\sigma \right)\right]/\left[\left({\alpha }_1+{\alpha }_2\right)\sigma \right]$$

(2)

where μ and σ are mean and standard deviation of each AE amplitude subset, found to be, respectively, ~45 and 8 dB, whereas ${\alpha }_1$ and ${\alpha }_2$ are user-defined coefficients representing lower and upper limits of the amplitude range in which the cumulative frequency–magnitude distribution properly fits a straight line. The Ib- and b-values formed by a 300-hit partitioning are plotted in Figure 5, showing a good accordance between the two analyses.

Besides the b-value, other synthetic parameters acting as potential fracture precursors can be extracted from a time series of N AE hits by the natural time analysis. This concept is introduced by ascribing the natural time χ_k = k/N to the k-th event of energy Q_k [25,26,27].

Regarding the normalized energies p_k ≡ Q_k/Σ_k=1^NQ_i as the probability distribution of the discrete variable χ_k, the variance ${\kappa }_1\equiv {\chi }^2-{\chi }^2$, is considered a key parameter for identifying the approach to a critical state, and defined as follows:

$${\kappa }_1\equiv {\displaystyle \sum }_{k=1}^N{p}_k{\chi }_k^2-{\left({\displaystyle \sum }_{k=1}^N{p}_k{\chi }_k\right)}^2\equiv ‹{\chi }^2›-‹{\chi }^2›$$

(3)

As χ_k and p_k are rescaled upon the occurrence of any additional hit, κ₁ results to be an evolutionary parameter.

It has been successfully shown that a variety of dynamical systems (2D Ising model [47], Bak-Teng-Wiesenfeld sandpile model [12,47], and pre-seismic electric signals [25,26,27]) become critical when κ₁, evolving hit by hit, approaches the value 0.07.

Two criteria were defined to identify the entrance of a system to true critical state [47,48,49,50]:

(1)

the parameter κ₁ must approach the value 0.07 “by descending from above”;

(2)

the entropies S and S_rev (entropy upon time reversal) must be lower than the entropy of uniform noise, S_u = 0.0966, when κ₁ coincides to 0.07. The entropy S is defined as

$$S\equiv ‹\chi \ln \chi ›-‹\chi ›\ln ‹\chi ›$$

(4)

where $‹\chi \ln \chi ›={\displaystyle \sum }_{k=1}^N{p}_k{\chi }_k\ln {\chi }_k$.

Here, the evolution of variance κ₁ and entropies S and S_rev of the natural-time transformed AE time series {χ_k} has been studied, where the event energy Q_k is derived from the amplitude A_k through the relation Q_k = cA_k^1.5, where c is a constant of proportionality [51,52]. Plotting all natural-time quantities as functions of the conventional time t provides a visual way to reveal the possible entrance point to “critical stage,” corresponding to the fulfillment of criticality Conditions (1) and (2). An entrance point to critical stage has been identified at time t_crit = 492 h (criticality initiation time, marked by a vertical dashed line in Figure 4 and by a vertical dotted line in Figure 6), i.e., 9 h before the b-value reaches its minimum. Remarkably, this critical point corresponds to the middle-height peak in the AE rate (highlighted by the dashed line before the highest peak in Figure 4) and to the appearance of high-amplitude AE signals.

This analysis suggests that the variance κ₁ of the natural-time transformed AE series can be identified as a pre-failure indicator, before the onset of non-reversible damage—supposedly revealed by the minimum b-value—within the bulk of the structural element.

4. Conclusions

The stability of a masonry wall of the Asinelli Tower has been assessed by the Acoustic Emission (AE) technique for a four-month period. The trend of the whole AE time series suggests that the monitored structural element is substantially stable, albeit with an ongoing damage process revealed by the AE activity observed over the entire monitoring period.

The observed correlation between the AE time series and the sequence of local earthquakes suggests that the local structural response is driven by the nearby seismicity. In particular, the densest AE cluster has been recorded within a few hours after the occurrence of the main local earthquake (4.1 magnitude). The b-value analysis of the AE cluster has revealed a significant, though momentary, acceleration of aging and deterioration processes in the monitored element, whose mechanical stability appears to be affected by light earthquakes.

Another emerging pattern is the transition of the monitored element to a state of criticality according to the paradigm of the natural time analysis [25,26,27]. The entrance to the critical state before the b-value reaches its minimum leads to consider the natural time variance κ₁ [47,48,49,50], as a possible early failure precursor. Future investigations in similar surveys would hopefully include the use of a seismometer, installed together with the AE system to record possible small seismic events affecting the observations.