Structural Ageing of a Cable-Stayed Bridge During Load-Test: The Overall Effect Monitored by Acoustic Emission

The focus of the present study is on material fatigue, consequent to load test. This newly constructed viaduct displayed an excellent performance. Hence, it is an effective and suitable reference to be compared with every old metal viaduct. In some respect, and up to some extent, this study also applies to concrete, or brick, or wood bridges. Indeed, fatigue is a permanently ongoing process and, when integrated over time, it affects old structures, causing progressive ageing and loss of performance and security. The difference between bridges constructed by different materials only relies on a different response-time to an applied tress. But fatigue and ageing are a much similar process when dealing with different materials. There is only need for a suitable calibration focused on every given case history.


Introduction
A study is here presented, which was carried out on a steel bridge monitored by acoustic emission (AE), during load-test before its opening to public. Other standard security checks of linear deformation were simultaneously carried out, according to law requirements, by laser monitoring.
The focus of the present study is on material fatigue, consequent to load test. This newly constructed viaduct displayed an excellent performance. Hence, it is an effective and suitable reference to be compared with every old metal viaduct. In some respect, and up to some extent, this study also applies to concrete, or brick, or wood bridges. Indeed, fatigue is a permanently ongoing process and, when integrated over time, it affects old structures, causing progressive ageing and loss of performance and security. The difference between bridges constructed by different materials only relies on a different response-time to an applied tress. But fatigue and ageing are a much similar process when dealing with different materials. There is only need for a suitable calibration focused on every given case history.
The technique here applied relies on passive AE monitoring in the ultrasound band. AE are spontaneously released by every stressed solid material. Indeed, AE occur as a response to every gentle stress, independent of its cause.
It should be pointed out that AE intensity is not of concern for the analysis which is here considered. The only requirement is that an AE signal is detectable. The timing of the AE release, not the intensity, is rather fundamental for the present analysis. specify the axial stress of several different components of the bridge, which were compared with direct measurements.    Only the details of Step 1 are here of concern. The vertical displacement of the key of arch (side A) was measured as -37 mm, which resulted 92% the model estimate -40 mm. The vertical displacement of the middle point of the road level (side A) was 59 mm, which equals 95% the computed 62 mm. The variation of compressive stress at the middle key of the arch (side A) resulted -3930 kN, which is 93% the model estimate -4243 kN. The external suspension cable 9e (side A) experienced a traction of 170 kN, which is 97% the estimated 175 kN. A lower oblique chain under the road level, which opposes the longitudinal and lateral extension of the arch, experienced a traction of 3160 kN, which is 89% the estimated 3560 kN. The sliding of the two western legs was (Δx, Δy, Δz, respectively, in mm): for the southern leg (-11,-1,0), to be compared with model computation (-12,-1,0), and for the northern leg (-11,0,0), to be compared with model computation (-12,1,0).
Similar results, which however are not here reported in detail, were found concerning Steps 2, 3 and 4 of the load test. The absolute values of all measured parameters resulted less than the estimated applied stress. They claim that this discrepancy derived from the size of the nodes of the arch, which in model computation were assumed point-like. Therefore, the model underestimated the true rigidity of the structure.
In general, the discrepancy between model and records resulted less than a few percent, which was explained by thermal dilation effects, originated by changes of air temperature. Owing to abrupt rain and hail, at the end of Step 1 an air temperature variation had occurred ΔT = -4°C which affected only the arch of the bridge, but not its road level, as it was protected by road cover. According to model computation, it was estimated that this effect implies a lowering to the road level by 4 mm. The discrepancy, 4 hour later, when the absolute value of ΔT had diminished, was only 2 mm. This result is consistent with the leading role of the thermoelastic stress, in agreement with what is clearly envisaged by the present investigation.
For future reference, the detailed load timing is here needed only concerning Step 1. Two trucks at a time were loaded, starting at 08 h 07 min a.m. (LT=UT+1 hour), attaining full load at 08 h 45 min 45 sec . The loading occurred by adding 3 sets of mixers at a time. The first set, here called "load-1" set, involved 7 couples of trucks loaded during 9 min (approximately at 08 h 07 min , 08 h 08 min , 08 h 10 min 45 sec , 08 h 12 min , 08 h 13 min , 08 h 15 min , 08 h 16 min LT). Then, 2 couples of trucks were loaded after a while (approximately at 08 h 24 min and 08h 34 min 15 sec ); this is here denoted as "load-2" set. The remaining 6 couples of trucks were loaded during 5.5 min (approximately at 08 h 42 min , 08 h 43 min , 08 h 43 min 30 sec , 08 h 45 min , 08 h 45 min 45 sec ), and this is here denoted as "load-3" set.
The load test further continued through Steps 2, 3 and 4. But, their detailed timing is not of interest for the present study. The entire load test was completed by late afternoon.

AE monitoring
AE were recorded (figure 5) at the base of the single eastern "leg", in two frequency bands: high frequency (HF AE) at 200 kHz and low frequency (LF AE) at 25 kHz. Per each frequency, the primary signal was released by a piezoelectric acoustic transducer. The signal was then pre-amplified and amplified. The rms amplitude of the signal was averaged over 5 msec. The entire set of all these [5 msec]-averaged signals was averaged over a pre-chosen time interval Δt. Then, a data logger stored this final average over Δt into two distinct data series, for HF AE and LF AE, respectively.
The main time series of records lasted between Dec 16 th 20 h 58 min 59 sec through Dec 29 th 14 h 17 min 35 sec . Data were collected at Δt=4 sec and these series are here briefly denoted as the "4s" data set. It is almost uninterrupted, apart a few minor gaps. During one of these gaps, between Dec 20 th 12 h 14 min 58 sec through Dec 20 th 13 h 39 min 11 sec , data were recorded with Δt=1 sec and these series are here briefly denoted as "1s" set.
Meteorological conditions were substantially perturbed, with occasional relevant wind gusts, and episodic rain or hail precipitation. However, no anemometer was available, and no regular temperature record.

Data analysis: Algorithms and physical principle
Data handling was carried out by a set of a few different algorithms. Reference is made to previous literature 6 . Several applications of these methods already appeared in previous papers by the authors and co-workers, mainly concerned with the natural environment (crustal stress and volcanic precursors), but including also a few studies dealing with laboratory test, either on steel or on (non-reinforced) concrete.
The present paper is specifically focused on the output of a few algorithms, which are better suited to characterize the overall performance of the steel structure. Additional algorithms are to be later considered by additional investigations (in preparation), to be more specifically concerned with detailed features of the time-history of the response by the microcrystalline solid structure to the applied stress, both during load-time and during after-load recovery.
The identical data handling and analysis has been separately applied to both HF AE and LF AE series.
One key algorithm, here applied and briefly summarized, deals with the fractal dimension D t of the time series of the AE records.
But a preliminary needed step is the outlier rejection which is applied to every AE raw data series. The purpose is to get rid of every AE signal that, owing to any physical reason (maybe sometimes even by unpredictable instrumental bad functioning but also by any other unwanted physical disturbance), eventually appears to deviate by a relevant amount with respect to some "smooth" trend of its background. However, while dealing with every previous analogous AE investigation, the outlier series resulted not to be concerned with spurious and unwanted disturbances. Rather, it reflected an intrinsic physical feature, derived from the intimate physics of the microcrystalline structure of materials (see section 4). This same conclusion is also found in the present study.
The subsequent investigation of the outlier series, which is here reported, is then carried out by the algorithm "arp", which in the present application resulted particularly suited for the detection of some (maybe unexpected) oscillations of the bridge.
The algorithm for outlier rejection relies on some mathematical technicalities, which are not of specific interest for the present discussion. Therefore, owing to brevity purposes, they are not here explained. The interested reader may refer to the aforementioned literature.
Call f (t) the data series of the records (of either HF AE or LF AE). It is a discrete set of values. In general, all values refer to successive time instants defined by a time increment Δt. According to the requirements by our algorithm, however, this regularity is only optional. For the 1s set it is Δt = 1 sec, and for the 4s set it is Δt = 4 sec. Reject the outliers.
Call f (t) a (weighted) running mean, computed only by means of the non-rejected f (t). In the present analysis, a triangular weight-function was chosen with half-time interval ± 100 sec. This interval, however, may be arbitrarily changed inside comparatively loose constraints, and this choice results to imply only a physically insignificant consequence on results.
Call g(t) = f (t) -f(t) the residual, computed by means of all f (t), i.e. including also the formerly rejected outliers.
Define a point-like process 7 identified with the time series of "AE events" defined as follows.
An "AE event" is identified with one relative maximum of g(t). But the amplitude of this relative maximum must to be above some arbitrarily pre-defined threshold, defined as follows.
Consider a reasonably wide subset of the original series of g(t). Call "S" this subset. Compute the rms value σ of all g(t) contained in "S". In the present case, the aforementioned threshold has been chosen as [σ/4] for the reasons explained below.
Choose another arbitrary and suitable time interval Δt 1 , which is used to evaluate D t . For every given pre-chosen time instant t j (for j=1, 2,...), consider the set "M" of all elements of the aforementioned point-like process, which occur inside a moving time lag of total duration Δt 1 and centred at the given t j . Apply the box counting method, 8 and compute the fractal dimension D t (t j ) (for j=1, 2,...) of the set "M". This D t (t j ) is one leading parameter in the present discussion.
The criterion used for the definition of the aforementioned threshold began by choosing ten trial values for the threshold, everyone arbitrarily defined as [σ/k] (with k=1, 2,..., 10). The fractal dimension D t (k) was computed on the entire aforementioned subset "S", and for every given k.
Owing to physical reasons, if k is exceedingly large, a threshold chosen equal to [σ/k] results exceedingly small. The background noise is thus included and some false "AE events" enter into subsequent computation: owing to its mathematical definition, a large D t (k)~1 must therefore be found.
In contrast, if k is exceedingly small, [σ/k] results exceedingly large, and the threshold excludes several physically significant "AE events", which are erroneously likened to background.
Therefore, owing to mathematical reasons, the plot of D t (k) vs. k certainly is monotonic and decreasing. But, whenever a step-like decrease is observed on this plot, this denotes the correct k value, which excludes the entire background noise, while it keeps all values which are physically significant. Hence, this k defines the correct logical ''sieve'' that rejects noise and saves the physical significant information. The optimum choice was thus found to be k=4.
However, in the present data analysis -and concerning both 1s and 4s sets -it is convenient to consider the definition of Δt 1 from a different viewpoint. Let us refer to the order number of the elements of the point-like process, rather than to their respective time instant. In the present application, this makes no difference, as the original AE data series was recorded at constant time increments Δt.
Three choices have been made for each 1s or 4s set. Every single D t (t j ) was computed by means of N D elements, which are included in the aforementioned Δt 1 moving time lag. It was chosen either N D =600, or N D =1200, or N D =1800 elements. In the case of the 1s data series, this implies that the evaluation of every D t (t j ) was carried out by referring to running time intervals of total duration 10 min, 20 min, and 30 min, respectively. In the case of the 4s data series, this corresponded to evaluate a D t (t j ) by referring to time intervals of 40 min, 80 min, and 2 hours, respectively. These different choices of N D were considered, because a different N D eventually plays a relevant role when dealing with the error-bar and scatter of the time series of computed D t (t j ) (j=1, 2,...). The reason is the unknown response to unwanted disturbances, originated by several physical environmental perturbations (see section 5). This N D choice resulted comparably critical for HF AE, while concerning LF AE series it appeared robust.
As already mentioned, other algorithms for data analysis are to be considered (in preparation), which are more directly focused on details of the response of the microcrystalline steel structure. But, as far as the present analysis is concerned, only one relevant physical item ought to be here anticipated.
According to the so-called "hammer effect" (see Gregori et al., 2007), we found that, in the present AE records, the AE release almost always occurs only during the "recovery stage", rather than during the "hammer stage". That is, no AE release occurs while the material is subjected, on an instant basis, to an externally applied stress. Rather, the AE release occurs as soon as the micro-crystals recover during their (approximately) "elastic" response, after the former applied stress. But, owing to brevity purposes, no additional details can be here given.
Another algorithm used for the present study is the "arp" histogram 9 applied to both outliers time series. This algorithm may be applied to every point-like process. Every event is considered independent of its intensity, and only the time instant of its occurrence is considered. Call {t j } (j=1, 2,...) the time series of a point-like process, and call Δt j,k (j,k= 1, 2,....; k>j) the set of all possible time intervals between the time instants of any couple of successive (even noncontiguous in time) elements of the set {t j }.
"Arp" is the histogram of these Δt j,k (j,k= 1, 2,....; k>j). But, it is well known that a histogram can be drawn only after choosing a suitable elementary time increment Δt e on abscissas, such that all the elements that occur during every given time interval Δt e of the histogram are supposed to be associated with an identical occurrence instant of time. Practically, it resulted convenient to define Δt e equal to (1/10) the average of all Δt j,k (j,k= 1, 2,....; k>j).
As it can be easily shown (just try it), owing to definition, if the point-like process is a random series, its "arp" must look like a rectangular triangle, with a regularly decreasing trend. In contrast, if the system has some leading component characterized by a periodicity T 0 , its "arp" will display approximately the same roughly decreasing trend, and a scatter superposed on it with relative maxima at every abscissa hT 0 (h=1,2,...).
Denote by T any general value for an abscissa of "arp" abscissas and call n(T) its ordinate. The error bar of "arp" is expressed as n(T ) ± n(T ). Since this error bar depends on n(T), the assessment may eventually result ambiguous of the occurrence of a relative maximum of n(T). This drawback can, however, be easily avoided by considering the histogram defined by n(T ) ± 1 / 2, which has a constant error bar, and will be here briefly denoted as arp.
In the next section a concise summary is given of the primary physical principle. This is the basis for entire physical rationale of all previous algorithms. Section 5 deals with the analysis of D t and with the way to recognize and rebut unwanted environmental disturbances. Section 6 deals with the "arp" (or arp) analysis of each outlier series.

The physical rationale
No material exists that is either ideally "elastic", or ideally "plastic". Every time that every real approximately "elastic" and solid medium experiences a stress, it also experiences a fatigue. For instance, even a tenuous thermal deformation is a cause of ageing of the medium.
The fatigue, or ageing, of the material is manifested as a rupture of some crystalline bond. Whenever an additional stress is applied, new bonds yield. But, in general, these new ruptures occur close to formerly broken bonds, where the crystalline structure is comparatively weaker.
In this way, a true chain-reaction occurs. This is the physical explanation of the well known phenomenon of cleavage plane in a crystal.
Every time that a crystalline bond yields, some AE is released, which is propagated through the medium. The primary physical information of our method relies on the timing of the sequence of subsequent AE release, which is detected inside the medium.
It should be pointed out that the concern is not about the intensity of the AE signal. There is only need to assume that the signal has a sufficient intensity in order that it can be detected. Indeed, the recorded AE amplitude is controlled by several unknown factors, such as by the distance and intensity of the instant AE source, but also by the unknown and eventually timevarying damping of the signal between source and detector, etc.
In contrast, the timing of the detected AE signal results to be an information of paramount importance in order to check how the medium responds to an applied stress. In this way, the ageing of the medium can be effectively monitored, and its eventual loss of performance. The entire procedure is therefore purely passive, and no invasive action is required.
An important related concept deals with the frequency of the AE signal, which depends on the size of the micro-flaw, which is associated with the broken bonds: comparatively smaller flaws release comparatively higher frequencies. We cannot know the law that relates flaw size and AE frequency, but we do know that this is the physically correct rationale.
While the ageing process is in progress, small flaws coalesce into larger ones. A former population of comparatively smaller flaws thus progressively decays, while it generates an increasing population of larger flaws etc.
Define "flaw domain" (Gregori et al., 2012) the typical physical domain of a flaw, which is associated with the observed AE of a given frequency (although we do not know the real size of this flaw domain). The statistics of flaw domains for a given AE frequency shall display a lognormal distribution. This inference derives by consideration of the rationale of the simplest case history of the socalled Kapteyn class distributions (Kapteyn, 1903(Kapteyn, , 1912Katpeyn and van Uven, 1916;Paparo and Gregori, 2003). That is, the probability of occurrence of an event is proportional to the number of identical events that are occurring at the same instant of time. For details and reference see the aforementioned literature. Owing to definition, a lognormal distribution is asymmetric. It has a tail, and this can be promptly shown to be the primary physical cause for the aforementioned persistence of outliers, both in f (t) and in g(t), independent of the "sieve".
We know therefore that one and the same kind of anomalous behaviour is to be expected to be observed first by AE of comparatively higher frequency, and subsequently by AE of every progressively lower frequency, etc. This is of paramount important, as it provides us with a physical information on the direction of the time arrow inside the ageing process. That is, we can thus recognize a precursor phenomenon compared to an after-event occurrence. For instance, in the case of seismic precursors, or of any kind of other environmental measurements, the practically unsolvable problem is well known of the assessment, on a statistical basis, of what is a precursor compared to what is an aftershock.
Summarizing, it is possible to monitor the ageing of a material -and the loss of performance of a structure (either natural or manmade) -simply by a passive monitoring of the AE released by its medium, when it responds even to a very gentle stress.
When an AE experiment is carried out in the laboratory, we can very effectively control the physical system, and by this we can minimize the impact of unwanted disturbances. In contrast, when operating in the field, this is impossible, and it is therefore important to record environmental perturbations in order to assess their respective impact on the AE records and on their interpretation.
While exploiting the AE monitoring of the Garbatella bridge, unfortunately no regular meteorological records were available. Hence, the meteorological disturbances had to be assessed by means of an a posteriori analysis on both AE data series.
In this respect it has to be pointed out that we deal with D t which is treated like a performance index. Its temporal trend is considered and, on its basis, an eventual alert is to be issued according to some pre-defined and well assessed protocol.
But, in general, while evaluating the D t vs. t trend, two distinct operative case histories are thus to be envisaged.
• In one case, every AE event primarily responds to one applied stress impulse, which is originated by an external action applied to the system. For instance, consider the case history of a volcano. Its endogenous hot fluids eventually repeatedly and progressively increase their pressure. The pores of the medium of the volcanic edifice experience an ever increasing number of yielding of flaw domains. As long as the solid structure of the medium affords to sustain the increasing pressure, it is found that D t remains reasonably small. But, when the pressure increases, also D t shall increase, as an ever increasing number of flaw domains will randomly yield per unit time. When D t increases until reaching 1 the volcanic edifice shall unavoidably yield, and a new boca is opened. This time sequence was observed e.g. on the occasion of the recent Stromboli paroxysm .
• The second case history is to be considered when the externally applied stress is only a trigger, and we observe only the subsequent evolution of the medium, while it searches for a new equilibrium state, after having suffered by the previously applied stress. In this case, a "young" medium first responds with a D t close to 1, because the ruptures of its bonds occur randomly, as no previously organized flaw domains exist inside it. In contrast, an "aged" medium will display a progressively decreasing D t and the lower is D t the more "aged" is the medium.
For instance, while carrying out experiments on some steel bars (Biancolini et al., 2006), it was found that when D t ~ 0.45-0.5 the bar is very close to break (different steels ought, however, to be tested in the laboratory, in order to assess an eventually different security threshold for different alloys).
Differently stated, D t denotes how far every AE event keeps a memory of other AE events either that occurred before it, or that are going to occur after it. No memory exists in a random sequence of AE event, the medium is therefore "young", and it is found D t =1, just due to the mathematical definition of randomness. When the medium suffers by progressive ageing, its flaw domains get progressively organized towards the final organization of a cleavage plane. This entire process is illustrated and quantitatively measured by the time evolution of D t towards progressively lower values.

Steel ageing -The D t analysis, and the rejection of environmental disturbances
Concerning the AE monitoring of the Garbatella bridge, for clarity and brevity purposes let us anticipate a few much general inferences and conclusions.
A higher temporal resolution ought to be recommended. An AE datum ought to be recorded, at least, every 50-100 msec (rather than every 1 sec or every 4 sec).
Consider the warning of section 4. When the external trigger caused by an environmental agent is repetitive, displaying some peculiar time sequence, the resulting AE signal -when it is interpreted according to the present rationale -may eventually simulate a false effect. Therefore, while one operates in the field, a sum of unknown and unpredictable disturbances must always be suitably taken into account, and whenever needed rejected.
This drawback is found to be particularly severe for HF AE, which are much more directly related to the primary external input. In contrast, owing to physical reasons (see section 4), the LF AE are more directly related to the downgrading of the crystalline structure. Indeed, LF AE are released when the material has already evolved and some conspicuous amount of comparatively large flaw domains have already been generated. Therefore, LF AE are to be expected to be much more indicative of the real loss of performance of a structure, while HF AE ought to be much better representative of the diachronic history of its external disturbances.
In terms of an expressive analogy, it is like listening music while a child close to you abruptly and loudly cries. The child noise has to be rebutted in order to appreciate the music in the background. Similarly, the ageing of the structures can be appreciated only after rejecting unwanted, even "loud", disturbances.
Summarizing, the primary scope of the analysis of a data series measured in the field is the distinction between the effects associated with the unknown timing of some external input, compared to the time history of the AE release determined by the evolution of the ageing process inside the medium which is to be monitored. In addition, the "perturbation" by external causes, which may eventually simulate a false behavior, is much better evidenced by means of HF AE compared to LF AE. 10 One additional relevant concern, related to the role of the external trigger, deals with a technological problem, i.e. with the time required by the whole AE recording device to reach its operative regime. During a limited initial time-lag, a sum of several normally unknown factors apparently perturb the AE records. This lag has to be empirically determined, mostly whenever one wants to carry out once in a while a rapid test of performance of a given structure (the purpose is to avoid, sometimes and whenever possible, a steady AE monitoring, which is comparatively more expensive and time consuming).
Summarizing, we have to distinguish (mainly for HF AE but also in LF AE) between AE signals caused by an accidental trigger compared to the AE signals which are passively released by the material and are specifically suited to monitor its ageing.
It is therefore here first shown how we first assessed the role of a few typical and relevant disturbances. The Garbatella bridge is "young" and performing. The target of the present testexperiment is therefore to calibrate the procedure of AE analysis, in order to check and assess a general procedure suited to investigate the performance of every old bridge.
We thus realized that -compared to the time of its formal load test -the viaduct suffered by a comparatively greater stress during the previous day, when the road cover was laid down. Figure 6 is a plot of the raw signal for both HF AE and LF AE 4s sets, while the 1s set is discussed only here below, when dealing with a specific item (see figure 22). An exponential decay trend is superposed on either plot to represent the recovery of the bridge after the stress that was applied during Dec 16 th and 17 th . The HF AE time-constant of the decay is about half the timeconstant for LF AE, consistently with the fact that HF AE, compared to LF AE, are more directly associated with a shorter-lived effect.
For future reference, it should be pointed out that the HF AE signal is very low, almost null (although not strictly null; see below) except during the warmer hours of the day (say between noon and 5 p.m.). This denotes that the signal amplification was insufficient in order to detect the AE signal other than when the thermoelastic deformation was conspicuous. This is a typical case history that shows that the instrumental amplification of the original AE signal was suitable only during some hours of the day, while during other hours the recording system was in underflow.
The most important inference which deals with material ageing is represented by D t (t j ) computed for LF AE and by the 4s data set ( figure 7). The three different computations, by N D =600, or N D =1200, or N D =1800 for every D t (t j ) computation, result remarkably similar.
Every apparently much dramatic very low value for D t (t j ) is the expected response to every sporadic disturbance originated by finishing works in progress on the viaduct. The viaduct was not open to public, and a conspicuous amount of finishing activity was in progress during the ~ 13 days spanned by the 4s set. Drills were occasionally used, operated inside either the metal components or the concrete basement of the "legs". Since the bridge is a very efficient AE probe, composed of a monolithic body with an excellent conduction of ultrasounds, the action of a drill -or of any kind of strong friction which causes some relevant local destruction of crystalline bons -must produce an LF AE signal with some very low D t (t j ) . This is the same effect as the aforementioned "loud" disturbance by the cry of a child while you listen music.
Another cause of much dramatic very low value for D t (t j ) is the eventual underflow of the AE detection device. Indeed, if the recorded AE signal is e.g. constant in time (e.g. at its lowest sensitivity value, i.e. 1 mV on the scale plotted in the figures here shown), it is found D t (t j ) = 0. This can be formally checked, but it also represents the fact that, when all AE records are identical, the physical system has a complete memory of all AE records which occur at every other instant of time.
Note that all these features are evident independent of N D . The algorithm is robust. The real relevant information about the ageing of the metal components of the viaduct is therefore represented by the long-range trend of the average value of D t (t j ), which is found to be intuitively close to D t~ 0.8.
The analogous D t time series for HF AE, shown in figure 8, denotes a comparably less robust response to the N D choice, but no clear inference. When the AE recording system is underflow (see figure 6) no D t can be computed, according to the argument mentioned here above. Figure 8 displays therefore an approximately diurnal periodical trend, because the system detects AE signals, with a significant time-varying intensity, only during the warmer hours of the day.
Therefore, we smoothed the D t (t j ) data series by means of a weighted running average, with triangular weight over 6 min 40 sec. The result for HF AE is shown in figure 9, which displays three time intervals with comparably much different trend. The initial and final time intervals appear to be steadily increasing. At present, it has been impossible to envisage the physical reason of this behaviour. Environmental disturbances ought to be monitored, dealing either      The same procedure was applied to the LF AE data series. Figure 10 shows quite a different result. No regular exponential decay is anymore clearly detectable. Rather, the steel responds abruptly to every temporary time-varying externally applied stress. This is particularly evident on Saturday Dec 24 th , Sunday Dec 25 th , and Monday Dec 26 th , because, owing to Christmas' holiday, basically no working activity was in progress on the bridge, which was rather subjected only to atmospheric disturbances. This means that HF AE, compared to LF AE, reflect a substantially much different feature of steel behaviour. HF AE reflect some much preliminary response, compared to LF AE which rather detect the substantial subsequent implications for crystalline structure, which are manifested as a later consequence of the primary applied external stress.
In any case, the prompt performance and reliability appears evident of this "young" viaduct, even during this much disturbed period of time, because the steel response denotes a rapid recovery after every applied stress, which promptly brings back the D t (t j ) value to a high and reliable level. Therefore, the medium is performing, even though the bridge, as a whole, has a slow recovery, as displayed in figure 6. In contrast, in the case of an older bridge, it is reasonable to expect that the steel ought to result much less performing, being denoted by a lower mean D t trend.
In this respect, two laboratory tests ought to be recalled. A perfectly "young" material has an ideal abstract value D t (t j ) = 1. In contrast, its ageing is monitored by the relative decrease of D t (t j ). An experiment on some suspension blades of martensitic steel (Braccini et al., 2002) showed a progressive decrease from D t (t j )~ 1 (when the blade was never bent after melting) to D t (t j )~0.6 (after it had been bent only a few times). Then, the crystalline structure of the martensitic steel apparently attained its working regime. Thus, it finally displayed a steady performance.
Only after some heavy and repeatedly applied stress, a steel bar is to be expected to break. Experiments carried out on small steel bars (Biancolini et al., 2006) were pushed until final rupture of every specimen. It was thus found that that when it is D t (t j )~0.45 -0.5 the steel is almost close to total rupture. It should be stressed, however, that these alert values ought to be calibrated for every specific steel alloy.
Hence, it has to be expected that, in the future, the D t (t j ) of the Garbatella bridge ought to decrease until reaching a standard and steady working regime [maybe D t (t j )~0.6 if the same threshold applies for the steel of the viaduct compared to the steel of the aforementioned laboratory experiment on martensitic blades]. This D t (t j )~0.6 will characterize its performance during the largest part of its existence. In contrast an old bridge, with collapse hazard, ought to have already slowly approached its final alert threshold of D t (t j ). It should be always stressed, however, that this threshold has to be assessed, in every case history, upon considering the specific kind of steel by which it was constructed.
As far as the cause of the scatter is concerned of raw data and of D t (t j ), no anemometer records were available. Hence, the role of wind can be only indirectly investigated in the present study. During those days strong gusts of wind frequently occurred. According to the personal witness of the two co-authors (SP and GV) who set up and operated the instruments, on the occasion of every wind gust the recording device experienced strong transient perturbations, mostly in HF AE. Hence, they tuned the signal amplification on these wind gusts, and the HF AE recording device later resulted in underflow during calm periods, with low thermal excursion.
In any case, as far as the available AE data are concerned, several different specific kinds of disturbances can be distinguished and recognized as explained in the following subsections. During Dec 17 th (red line), at ~8 a.m., the load-test was started, with dramatic consequences on the LF AE signal. Note that the straight line is associated with a period of time during which no records were available, due to a temporary failure of power supply.

Thermoelasticity, and the effect of a time-varying load
During the subsequent days, the most intense LF AE signal was recorded during working hours (say roughly between 8 a.m. through 5 p.m.), envisaging an effects associated with the stress applied while finishing the bridge.
But, it appears curious the fact that also on Dec 25 th , Christmas Day, when no work was ongoing on the bridge (yellow line), some relevant LF AE signal was observed. In addition, in general, on every day a comparatively more intense signal was recorded almost at the same local time, i.e. during the early afternoon until ~ 4 p.m. Therefore, this appears to be a likely thermoelastic effect.
In addition, in general a reasonably ordered and regular scatter was observed every day before 7 a.m. (except on Dec 17 th , when the bridge was recovering after the stress of the previous day).
In contrast, the comparative trend on different days after 6 p.m. appears more varied, maybe depending on different air temperature (for which, however, no record is available).
All these features are suggestive of a thermoelastic effect, which, in principle, ought to be expected to be manifested in two different ways.
On the one hand, a thermoelastic effect -which is certainly conspicuous on concrete or brick bridges -is similar to what is observed on the Gran Sasso mountain data series (a massif in central Apennines) by AE records measured in a deep cavern ; Gregori and Paparo, 2004; Gregori et al., 2012). This effect is the consequence of the cooling and/or warming of the shallower layers of the rocks (limestone and dolomia) of the mountain. This cooling or warming involves first the outer layer, and later on the deeper layers. When the body warms up, the outer layer experiences thermal expansion, while it overlies colder and thermally more contracted inner layers. In contrast, when the body cools off, the outer layer shrinks due to thermal compression, while the inner layers are still warm and more expanded. Hence, the outer layers have insufficient room, and some crack will occurs in the outer layer. The phenomenon is the same as what happens to the furniture of a non-heated house, during the cold early-morning hours in winter time. Or this is the same well known phenomenon which typically occurs to rocks in an extreme desert area, etc.
Since, compared to a metal, concrete and bricks have smaller thermal conductivity, the thermoelastic degrading is expected to be comparably more relevant in concrete or brick bridges. And this effect is likely to be maximum when the thermal gradient is comparatively larger during the cooling process, i.e. during the early hours of the day. This is the aforementioned effect observed on Gran Sasso.
In contrast, when dealing with a metal structure, a different behavior ought to be observed. The linear elongation of the large metal components of the bridge is the cause of large displacements of the supporting points of every bridge element (during the aforementioned Step 1 of the load test the bridge elongated by 11 mm). This phenomenon ought to be comparatively larger when the absolute value of either the warming or the cooling process is maximum. This maximum (cooling) occurs during the first few hours afternoon. This effect ought therefore to be comparatively more relevant on metal bridges, compared to concrete bridges. This is observed on the Garbatella bridge.
Therefore, whenever temperature records are eventually available during AE monitoring of a bridge, constructed either by concrete or by bricks or by wood or by metal, the temperature gradient ought to be considered, and the response of the AE signal is different depending on the thermal conductivity of the material.
Since violent time-variations of the LF AE signal occurred also during the days when the working activity was totally (or almost totally) absent due to Christmas holiday, the phenomenon ought to be only -or almost only -thermoelastic.
Consider that this thermoelasticity implications were here observed on a bridge in Rome, where a mild and temperate climate is normally enjoyed. The thermoelastic effect has therefore to be expected to be much more important, in terms of ageing hazard, in the case of a bridge located in some comparably more severe environment.
For completeness sake, the HF AE figure analogous to figure 11 is shown in figure 12, which plots raw HF AE data in a 24-hour cycle diagram. In general, the AE signal was recorded only during the warmer hours of the day, when a thermoelastic effect was active.
Note, however, that after Dec 16 th , ~ 21 p.m. through Dec 17 th ~ 6 a.m. the viaduct was recovering after the heavy stress of roadbed deposition, and the AE signal was therefore conspicuous.

Figure 12.
Raw HF AE data, 24-hour cycle diagram. In general, the AE record were underflow except during the warmer hours of the day, when a thermoelastic effect was active. But, after Dec 16 th , ~ 21 p.m. until Dec 17 th ~ 6 a.m. the viaduct was recovering after the heavy stress of roadbed deposition, and the AE signal was therefore conspicuous. In addition, during Dec 24 th , between ~ 21 -23 p.m., some environmental disturbances, i.e. likely wind gusts, produced clearly detectable AE signals. Figure 13 shows a 24 hour cycle diagram of D t (t j ) of the HF AE 4 sec data set. Figure 13 displays a comparably confused trend. There is, however, some large effect, which seems thermoelastic. Also the effect of hail is observed (see section 5.5). But, several most prominent disturbances appear uncorrelated either with Sun hours during the day, or also with working days, as during this period of time several days were total holiday. Hence, these disturbances are very likely to be associated with strong wind gusts that frequently, and more or less erratically, occurred during those days in Rome.

Wind gusts
Therefore it is reasonable to conclude that wind gusts play a definitely relevant role in metal ageing, even on a bridge that has a structure which is likely to exert a limited aerodynamic opposition to wind.
The plot analogous to figure 13, but referring to LF AE is shown in figure 14, which is shown only for the sake of completeness. But no apparent regularity is observed. The trend appears definitely less influenced by the thermoelastic effect. The excellent performance of the viaduct is shown by the D t values comprised between ~ 0.6 and ~0.95. But, during the afternoon some finishing works were being carried out, corresponding to lower D t values. However, the anomalous low value of D t occurred between 04:45 and 04:50 LT of Dec 22, and it clearly corresponds to a period when the LF AE was constant and underflow. Hence, as mentioned in section 5, it is found D t (t j ) = 0.

Trains
Trains frequently transit under the bridge, moving either slowly (say at < 10 km / hour) or faster (say at ≥ 50 km / hour).
The disturbance caused on the bridge depends on train speed v according to the following approximate order-of-magnitude estimate. Call m the total mass of displaced matter. If one considers the air blast caused by the train, m is the air mass which is contained inside an air volume equal to the volume of the train. Instead, if one considers the impulse caused by the mass of the train while it crosses on the railway under the viaduct, m is the mass of the train.
In general, it appears more likely to associate the AE disturbance to the shock-wave by air blast, better than to the soil shock caused by train's load. But, if an anemometer is available on the bridge, this dilemma can be promptly solved (see below). In any case, in either case the same following approximate argument can apply. It is found that urban metro trains produce no sensible effect, as they move very slowly due to their regular stop at the Garbatella station. Only the suburban trains eventually transit at a comparably higher speed, and may cause a detectable effect. Consider also that the train crosses under the bridge at a level which is comparable with the entry of a high-speed train into a tunnel.
According to the official time  figure 15 are indicated every 0.005 hours.
If the air blast of a train is responsible for this effect, a similar effect ought to be observed for a wind gust. Hence, an anemometer located close to the bridge -and also close to its western terminal, where the railway is located and were the AE records were collected; see figure 1should clearly evidence the role of a perturbation on the bridge that is caused either by a wind gust or by a blast-wave by a train.
This datum is interesting for high-speed railways. When a high-speed train (with v ~ 300 -400 km/hour) enters or leaves a tunnel, the impact of its shock-wave is ~ 900 -1600 times the impact of the shock-wave caused by a train with v ~ 10 km/hour. This is responsible for a conspicuous ageing of the nacelle of the train. But, the same shock is applied also to the walls of the tunnel, which thus also experiences a corresponding ageing and potential security performance. Figure 16 shows D t (t j ) during load-test. For comparison purposes both HF AE and LF AE are plotted in the present and in the following figures. The correlation appears evident with the sequence of "load-A", "load-B" and "load-C" sets. In particular, while the bridge was recovering after the stress originated by the "load-A" set, a new stress was applied by the "load-B" set, etc. Figure 17 shows the same plot during a longer time interval, including D t (t j ) also during Dec 16 th , when the bridge suffered by a violent stress caused by roadbed deposition.  Figure 17 also shows a much anomalous effect close to Dec 17 th , 10 h 43 min (=17.44652 in day units). The cause was a short-duration hail storm (according to direct observation by the authors). The effect of hail grains is very small on the crystal bonds of the metal micro-structure of the bridge. While the hail storm is in progress, a tinkle is listened. But the AE transducer can record no audible signal. Rather it measures only HF AE and LF AE released by microcrystal bonds, which are stressed and broken by hail's impact. However, owing to the very feeble intensity of the effect, the time sequence of the AE records responds essentially only to the timing of different hail grains that hit the bridge at different sites. Hence, since these gentle strokes are essentially random, it must be expected to find D t (t j )≅1, which is indeed observed. Note that other similar D t (t j )≅1 periods of time were observed in those weeks, when additional hail storms occasionally happened in Rome.   That is, the two leading oscillation periods inferred by "arp" appear much different compared to model computation, although they are a clear and unquestionable observational evidence.

Hail
On the other hand, consider that with one AE record every 4 sec, or even every 1 sec, it is impossible to search for frequencies close to ~1 Hz. Hence, a much higher time rate in AE acquisition is strictly required in order to exploit a more pertinent check of the proper oscillation periods of a bridge with model computation.
It should also be pointed out that in the case of a volcano, e.g. of Peteroa (Ruzzante et al., 2005, the analogous "arp" plot (unpublished) shows, unlike in the present case history, a dramatic superposition of very many different proper oscillation periods. Indeed, in contrast   to every natural physical system, every manmade structure responds to a specific "simplicity" rationale, according to some ordered geometrical structure, etc.
The ~ 53.798 sec oscillation is also displayed in figure 13, although superposed over the large disturbances originated by wind gusts or by thermoelastic effects. It is also confirmed by the 1s data set. Figure 22 shows D t (t j ) for HF AE of the 1s set, computed by means of 600, 1200, and 1800 data. The N D =600 case history oscillation appears closely correlated with the transit of the three "fast" crossing trains evidenced in figure 15. The most intriguing feature is evidenced by the N D =1800 data case history, which displays a resonance oscillation with a frequency with period ~ 1 min (between 59.87 sec and 61.15 sec), to be compared with the aforementioned ~ 53.798 sec oscillation. The same ~ 1 min period may be recognized also in the D t (t j ) LF AE 1s data series, although only with 1800 data, and with a substantially larger scatter, due to the less faithful LF AE monitoring, compared to the HF AE monitoring, of the external applied disturbance.
In either case, consider that the 1s set spans a short time interval, and the statistical dependence on N D results dramatic.
As far as the HF AE are concerned, figures 18 and 19 display a large maximum of "arp" corresponding to the diurnal variation (two peaks at ~1 day 7 min, and ~ 1 day 27 min) which is evident in figure 6, although it is mainly a consequence of underflow of the AE detecting device. No other intuitively clear periodicities are evidenced, and are to be investigated by a specifically devoted investigation (in preparation).

Conclusion
AE monitoring of a metal viaduct appears much effective, feasible, and practical. The same procedure, apart lesser changes in procedures, can be successfully applied also to every concrete or brick or wood bridge.
The recommendations are here summarized, which ought to be taken into account when implementing an AE monitoring on a viaduct.
What parameter should be monitored?
LF AE are certainly much better suited to monitor the overall bridge performance. In general, HF AE may appear comparably less useful. However, HF AE can result important -or sometimes even crucial -whenever a more precise physical interpretation is needed while dealing with some unexpected or unwanted behaviour of materials.
In addition, regular records of meteorological and other environmental parameters ought to be monitored. Also the instant traffic load might be an important environmental information, although, in general, after a suitable calibration carried out once forever, the traffic signal is likely to be easily recognized by a simple routine AE monitoring alone.
What is the recommended time rate?
One rms time-averaged AE record, say, every 25-50 msec appears to be a good choice, upon considering costs for instruments and data handling, and also the detail which is required in order to detect the proper oscillations of the viaduct.
By this, all kinds of hazard can be safely monitored (except an eventual very rapid damage, such as caused by an explosion, which should require a much higher time rate; but in general this information is of no practical interest).
What is the best procedure for AE monitoring? In principle, AE monitoring can be operatively planned in three different ways: (i) steady permanent real-time monitoring operated from a remote control room; (ii) steady permanent monitoring with AE records stored by a data acquisition system, to be later recovered and analyzed; (iii) AE test carried out once-in-a-while either periodically or depending on particularly heavy environmental or traffic stress, etc.
The choice of either one procedure, or another, depends on costs and on the specific requirements by the user.
In general, real time remote monitoring may result less expensive, in terms of personnel and of routine automatic operation.
In addition, a once-in-a-while operation cannot be carried out on an instant basis. Indeed, in general one drawback is the time required by the AE recording apparatus to reach regime standard operation. In addition, environmental conditions, such as rain and subsoil water flow, may affect only on some days and not on others the long-term stability of a pillar of a bridge, etc. The same warning applies to every transient disturbance, such as wind gusts which occur only on some days, or a more or less intense diurnal thermal excursion, etc.
In addition, a real-time remote monitoring is also a warranty for a prompt alert about abrupt events that may severely affect the viaduct security (landslides, hurricanes, floods, terrorism, etc.).
How many AE devices are required on a viaduct structure?
In general one AE recording device is needed for every "monolithic" component of the bridge. By "monolithic" component it is here meant a unique solid body through which AE are effectively transmitted. For instance, a metal bridge is a unique huge metal body, and every AE, which is released at any point inside it, is promptly transmitted to all other parts of the bridge with negligible damping (at least as far as the size of the bridge in not exceedingly large).
In addition, the recommendations are to be taken into account provided by structural engineers, who should indicate the nodes that are likely to support the largest stress and are therefore the points that are more likely to suffer by a comparably more rapid ageing.
In any case, a given composite bridge in general has several pillars, and it is likely that AE cannot be easily transmitted from one pillar to the next. Hence, it is necessary to install an AE monitoring on every pillar. The same recommendation holds for every arch.
In addition, suitable consideration ought to be given for the connection of a bridge to ground on either one of its sides, mainly whenever there is also a tunnel immediately close to the bridge, etc.
In general, AE monitoring ought to be recommended to be simultaneously operated at different points on the viaduct. However, it is also possible to envisage a periodical AE test carried out at different times and on different pillars, nodes, etc. Instrumental costs may be reduced, but operational costs may result to be largely increased, and the detail is certainly reduced of the final information about loss of performance and about security.
That is, every case history has to be considered independently, and the costs for implementation and operation are to be optimized depending on the required kind of alert which is required by the user.
What is the relevant difference between a metal viaduct and a concrete or brick or wood viaduct?
The aforementioned "monolithic" component structure has to be taken into account when dealing with every kind of viaduct.
Concrete bridges are expected to suffer by the comparative more intense thermoelastic effect during the early hour of a cold morning, unlike metal bridges that suffer by thermal excursion mainly during the hotter hours of the day.
A present great concern deals with the unknown performance of concrete, when it is older than one century, mainly when its ageing is combined with the effect of some particularly hostile environment.
Brick bridges ought to be tested in order to assess how far AE can be transmitted between contiguous bricks depending on the specific kind of mortar that was used. In general, a brick wall has a much compact structure, and in general AE transmission is likely to result much effective. In addition, in general a wetting of materials may dramatically improve AE transmission, etc. Hence, every case history has to be suitably evaluated, and every aforementioned warning has to be considered, which also applies to metal or concrete bridges.
Wood bridges require no particular additional warning, other than the investigation and calibration of that specific kind of wood, when it is strained by an applied stress. Compared to metal or concrete or stone etc., wood behaves much differently depending on its fibrous structure, which determines its "elastic" or "plastic" response, and also some kind of comparably time-delayed final yielding and rupture.