PSI - Issue 55

Dimos Triantis et al. / Procedia Structural Integrity 55 (2024) 185–192 Triantis et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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to the minimum possible level, and, also, that it should be of reversible nature) and, in addition, the Continuous Struc tural Health Monitoring of the restored elements. Nowadays, the No Destructive monitoring technique most widely used worldwide is that of the Acoustic Emissions (AE). An extremely wide variety of parameters, obtained from the analysis of raw data concerning the acoustic signals, are used in order to characterize the damage level of a given structural member and, most importantly, to quantify the proximity of the system (loaded structural member or loaded structure) to the entrance into its critical stage, namely the stage during which macroscopic catastrophic fracture is impending. Among these parameters one could mention (indicatively only) some characteristics of the acoustic wave recorded, as it is, for example, the rise time (either its magnitude or normalized over the respective amplitude), the average frequency, the relation between the rise time per amplitude and the average frequency etc. In addition, one could mention the cumulative number of the counts recorded, the rate of production of acoustic signals (either hits or events), the b -value and the improved b -value (quantifying the relation between weak and strong events) etc. Recently, studies have been published which take advantage of additional parameters, namely, the interevent time intervals between any two successive acoustic signals (Triantis and Kourkoulis (2018)), the distance (Euclidean) between the sources of any two successive acoustic events, the average location of the acoustic sources and the energy (or the respective power) of the acoustic waves (Triantis et al. (2022a)) etc. In general, the analysis of the acoustic activity is implemented either in terms of the conventional time or in terms of the so-called Natural-Time Domain (Triantis et al. (2023)). Relatively recently, studies have been published attempting to analyze the data related to the acoustic activity using concepts based on the principles of Non-Extensive Statistical Mechanics (NESM), a scientific discipline that is found on the borderline between Physics and Applied Mechanics (Kourkoulis et al. (2023), Stavrakas et al. (2016)). The temporal variations of the above parameters provided by the AE technique during the process of loading and fracture of brittle building materials (as, for example, concrete and rock-like materials) have been long ago studied by many researchers worldwide. It has been indicated that signs warning about upcoming fracture can be detected by proper analysis of the data. Indicatively, one could mention the sudden increase of the rate of generation of acoustic hits and counts (Li et al. (2019), Ohtsu et al. (2005), Rao et al. (2009), Triantis et al. (2021), Triantis and Kourkoulis (2018), Vidya Sagar et al. (2013), Yan et al. (2023)), the abrupt decrease of the b -value and that of the Ib -value (Aggelis et al. 2011, Loukidis et al. 2021, Meng et al. 2016, Rao et al. 2005), the decreasing trend of the average frequency of the acoustic signals (Aggelis et al. (2011), Sun et al. (2017), Triantis (2018), Tsangouri and Aggelis (2019)), the intensely increasing rate of the energy content of the AEs and the respective cumulative energy (Cai et al. (2007), He et al. (2010), Pasiou and Triantis (2017)) etc. The latter, i.e., the average energy content of the acoustic signals is the object of the present study. The temporal evolution of the specific quantity is explored in terms of the time-to-failure variable (in other words, along an inverse time arrow), in an attempt to detect characteristics that could provide in formation about the proximity of the loaded system to its critical stage. The present analysis is based on experimental data gathered from previously implemented protocols, during which the acoustic activity generated while marble specimens were loaded either in direct tension or in uniaxial compression (until fracture) was recorded. The study indicates clearly that several seconds before the macroscopic fracture of the speimen the temporal evolution of the average energy of the acoustic events exhibits a clearly distinguishable plateau, which is terminated some tenths of a second before the final disintegration of the specimen. It is thus suggested that an additional pre-failure index is hidden in the AE data, an index that could be quite valuable in hands of structural engineers, especially if it is considered in parallel with already existing indices. The specific conclusion is verified by studying the temporal variation of the average energy of the acoustic events in juxtaposition to the respective variation of the Pressure Stimulated Currents produced while an accurate copy of a restored marble epistyle of the Parthenon Temple on the Athenian Acropolis (Athens, Greece) is loaded under multi-point bending. 2. Methods: the temporal variation of the average energy content of the acoustic events in the case of elementary tests Consider a time series of N acoustic events, generated at the time instants t 1 , t 2 , …, t N = t f , where the instant t f corresponds to the N th event, namely the event recorded at the fracture instant. The respective energy contents, E i , of each event form another time series E 1 , E 2 , …, E N . The average energy content of n successive events, ( ) , i E t and the total average energy content of all the events, ( ) , f E t recorded up to the fracture instant, are defined, respectively, as: