Issue 50

D. Triantis et alii, Frattura ed Integrità Strutturale, 50 (2019) 537-547; DOI: 10.3221/IGF-ESIS.50.45 540 1.E-07 1.E-06 1.E-05 1.E-04 0 20 40 60 80 100 time (s) average strain rate stage B stage D 1E-04 1E-05 1E-06 1E-07 Average strain rate [s -1 ] 8 1 Time [s] stage B stage D Stage B Stage D stage stag Figure 3: Time evolution of the average strain growth rate < Δε / Δt>, in stages B and D. E XPERIMENTAL RESULTS AND DISCUSSION Analysis in terms of the Ib-value and the cumulative energy of the acoustic signals he number of AE hits recorded during uniaxial compression tests on rocks is usually large with inconsistent shapes of the respective waveforms and with parameters varying within wide limits. In the present study AE hits with duration less than 10 μs and count number less than 2 were ignored [18], in order to exclude from the analysis AE hits that would probably be of parasitic nature. The number of AE hits, of amplitude equal or higher than 40 dB that were finally used after the above filtering, was equal to about 3500. For the specific experiment discussed in previous section, this number was equal to 3335. The allocation of these hits to each one of the four stages of the loading protocol is shown in Table 1, together with the average amplitude, the average energy and average duration of the hits of each stage. Stage AE hits number Average amplitude (dB) Average energy (aJ) Average duration (μs) A 893 49.3 3098 4734 B 730 48.0 621 1966 C 174 50.9 7027 11112 D 1538 49.7 25095 5645 Table 1: Statistical data for the AE parameters. To further explore the details of the acoustic activity, an improved b-value (denoted from here on as I b -value) analysis is carried out, as it was already discussed for the specific protocol by Triantis [16]. In this direction, the total number of AE hits was divided into groups of sequential hits. Each group included 100 hits and the sliding step was set equal to 1. This means that the first group (providing the first value of I b ) includes the first 100 hits (i.e., the hits with order from i=1 to i=100), the second group (providing the second value of I b ) includes the hundred hits with order from i=2 to i=101, etc. The I b -values were then calculated using the familiar equation:       1 2 1 2      log log N N Ib          (1) In Eq.(1) μ is the mean amplitude, σ is the standard deviation and α 1 , α 2 are constants the numerical value of which is usually set equal to 1 [1]. Then, each I b -value was paired to a time instant corresponding to the mean value of the time instants of occurrence of the hundred sequential hits of each group. The results of the above procedure are shown in Fig.4, in which the time evolution of the I b -value is plotted for all four stages of the loading protocol, in juxtaposition to the respective evolution of the cumulative energy of the acoustic signals. The abrupt reductions of the I b -values, towards levels approaching the critical limit of 1, observed in Fig.4, are always ac- companied by strong increase of the cumulative energy of the acoustic signals. This is observed as one approaches the end of stage A (when the stress exceeds about 90% of the fracture stress), during stage C and, finally, at the end of stage D during T