Issue 50

V. Saltas et alii, Frattura ed Integrità Strutturale, 50 (2019) 505-516; DOI: 10.3221/IGF-ESIS.50.42 511 (a) recording time: 12:00:00 (43200 sec) (b) recording time: 12:11:13 (43873 sec) (c) recording time: 13:29:37 (48577 sec) (d) recording time: 17:58:41 (64721 sec) Figure 7 : 3D location patterns of cumulative events at different selected times, during monitoring of the fracturing process in the concrete specimen. The numbered green dots indicate the positions of the 7 AE sensors. The cylindrical hole was drilled along the z-direction (refer to Fig.1). Axes scale is in mm. the cylindrical hole, due to its finite length and the absence of any confinement on the upper side of the hole. Thus, the expansive pressure should be higher in the inner part of the hole than at its edge. This results in the generation of micro- cracks starting from the inside and then extending towards the outside of the hole. As for the snapshot corresponding to the beginning of range C (Fig.7d), the distribution of the events has been further extended, due to the formation of macro- cracks in the concrete specimen (Figs.1(b,c)).Further estimation of the events localization should be no longer valid, as the specimen has started to be divided into 2 pieces (refer to Fig.1b). Non-extensive statistical analysis of acoustic emissions The concept of non-extensive statistical physics (NESP) has been successfully applied to the investigation of complex systems in different length-scales, such as earthquakes and fracturing experiments in brittle materials [24-29]. NESP has been introduced by Tsallis in order to describe the non-equilibrium stationary states of a system which exhibits long-range interactions, memory effects and multifractality [30,31]. In this context, Tsallis proposed replacing the classical Boltzman- Gibbs entropy with the generalized q -entropy (or Tsallis entropy) which is defined as: ௤ ൌ ௞ ಳ ௤ିଵ ൫1 െ ׬ ሾ ሺ ሻሿ ௤ ஶ଴ ൯ (3) where ஻ is Boltzmann’s constant, p ( X ) is the probability distribution function of the continuous variable X , and q is a real parameter which describes the degree of non-extensivity of the system under consideration. For q >1 or q <1, the system