Cyclic loading of marble: Correlating the attenuation of the electric and acoustic activities and highlighting criticality indices in terms of natural time

Abstract

The attenuation of the acoustic activity in marble specimens under uniaxial compressive loading-unloading loops is quantified in juxtaposition to that of the electric activity. In parallel, the existence of “pre-failure indices” warning about entrance into a critical stage, that of impending fracture, is explored. The acoustic activity is quantified in terms of the normalized number of acoustic hits, their average rate of production and their cumulative energy, and, the cumulative counts and their average rate of change. The electric activity is studied in terms of the pressure stimulated currents and the electric charge released. The analysis revealed that the acoustic and electric activities are linearly correlated to each other, suggesting that they are different manifestations of the same damage mechanisms. In addition, Kaiser’s effect, governing the acoustic activity, is found to govern, also, the electric activity. Moreover, it is concluded that entrance into the critical stage is safely predicted by means of a simple criterion, based on the evolution of the average rate of change of the normalized cumulative counts in the natural time domain. These predictions are almost identical with those of the criterion based on the “variance” and the “entropies” of the time series of acoustic events in this domain.

Keywords

Marble cyclic loading / Acoustic emissions / Kaiser’s effect / Pressure stimulated currents / Criticality indices / Natural time

Acknowledgements

The authors would like to sincerely thank the reviewers for the time and effort they spent to critically and productively review our original manuscript. Their comments and suggestions contributed to the improvement of the quality and scientific integrity of the study. This contribution is kindly acknowledged.

References

[1] Grosse C, Ohtsu M. Acoustic Emission Testing. Heidelberg: Springer; 2008.

[2] Ohtsu M. History and fundamentals. In: AcousticEmission Testing. Cham: Springer International Publishing; 2021. p.11-20.

[3] Aggelis DG, Shiotani T. Parameters based AE analysis. In: AcousticEmission Testing. Cham: Springer International Publishing; 2021. p.45-71.

[4] Triantis D, Pasiou ED, Stavrakas I, Kourkoulis SK. Revealing the proximity of concrete specimens to their critical damage level by exploring the cumulative counts of the acoustic emissions in the natural time domain. Materials 2024; 17(5):1017.

[5] Varotsos PA, Sarlis NV, Skordas ES. Long-range correlations in the electric signals that precede rupture. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 66:011902.

[6] Cartwright-Taylor A, Vallianatos F, Sammonds P. Superstatistical view of stress-induced electric current fluctuations in rocks. Phys A Stat Mech Appl 2014; 414:368-77.

[7] Stavrakas I, Triantis D, Agioutantis Z, Maurigiannakis S, Saltas V, Vallianatos F, Clarke M. Pressure stimulated currents in rocks and their correlation with mechanical properties. Nat Hazards Earth Syst Sci 2004; 4(4):563-7.

[8] Li ZH, Wang EY, He M. Laboratory studies of electric current generated during fracture of coal and rock in rock burst coal mine. J Min 2015; 2015(1):235636.

[9] Li DX, Wang EY, Li ZH, Ju YQ, Wang DM, Wang XY. Experimental investigations of pressure stimulated currents from stressed sandstone used as precursors to rock fracture. Int J Rock Mech Min Sci 2021; 145:104841.

[10] Shan TC, Li ZH, Zhang X, Zhou X, Cai C, Tian H, Ding Z, Zhang Q, Zang Z, Ali M. Experimental study on pressure stimulated current response characteristics during damage evolution of water-bearing coal samples. Bull Eng Geol Environ 2023; 82(4):128.

[11] Aydin A, Prance RJ, Prance H, Harland CJ. Observation of pressure stimulated voltages in rocks using an electric potential sensor. 2009; 95(12):124102.

[12] Archer JW, Dobbs MR, Aydin A, Reeves HJ, Prance RJ. Measurement and correlation of acoustic emissions and pressure stimulated voltages in rock using an electric potential sensor. Int J Rock Mech Min Sci 2016; 89:26-33.

[13] Li ZH, Zhang X, Wei Y, Ali M. Experimental study of electric potential response characteristics of different lithological samples subject to uniaxial loading. Rock Mech Rock Eng 2021; 54(1):397-408.

[14] Shan TC, Li ZH, Jia HS, Wang EY, Wang XR, Niu Y, Zhang X, Chen D, Yin S, Zhang QC. Failure evolution and disaster prediction of rock under uniaxial compression based on non-extensive statistical analysis of electric potential. Int J Min Sci Technol 2024; 34(7):975-93.

[15] Eccles D, Sammonds PR, Clint OC. Laboratory studies of electrical potential during rock failure. Int J Rock Mech Min Sci 2005; 42(7-8):933-49.

[16] Nitsan U. Electromagnetic emission accompanying fracture of quartz-bearing rocks. Geophys Res Lett 1977; 4(8):333-6.

[17] Scoville J, Sornette J, Freund FT. Paradox of peroxy defects and positive holes in rocks. II. Outflow of electric currents from stressed rocks. J Asian Earth Sci 2015; 114:338-51.

[18] Slifkin L. Seismic electric signals from displacement of charged dislocations. Tectonophysics 1993; 224(1-3):149-52.

[19] Vallianatos F, Tzanis A. Electric current generation associated with the deformation rate of a solid: Preseismic and coseismic signals. Phys Chem Earth 1998; 23(9-10):933-8.

[20] Pasiou ED, Triantis D. Correlation between the electric and acoustic signals emitted during compression of brittle materials. Frat Ed Integr Strutt 2017; 11(40):41-51.

[21] Saltas V, Vallianatos F, Triantis D, Stavrakas I. Complexity in laboratory seismology:From electrical and acoustic emissions to fracture. In: Complexity Measurement and Application to Seismic Time Series, Measurement and Application. Amsterdam: Elsevier; 2018. p.239-73.

[22] Triantis D, Pasiou ED, Stavrakas I, Kourkoulis SK. Hidden affinities between electric and acoustic activities in brittle materials at near-fracture load levels. Rock Mech Rock Eng 2022; 55(3):1325-42.

[23] Kourkoulis SK, Pasiou ED, Dakanali I, Stavrakas I, Triantis D. Notched marble plates under tension: Detecting prefailure indicators and predicting entrance to the ‘‘critical stage”. Fatigue Fract Eng Mater Struct 2018; 41(4): 776-86.

[24] Shan TC, Li ZH, Zhang X, Jia HS, Wang XR, Wang EY, Niu Y, Chen D, Sun WC, Wang DM. Pressure stimulated current in progressive failure process of combined coal-rock under uniaxial compression: Response and mechanism. Int J Min Sci Technol 2024; 34(2):227-43.

[25] Ma LJ, Liu XY, Wang MY, Xu HF, Hua RP, Fan PX, Jiang SR, Wang GA, Yi QK. Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 2013; 62:34-41.

[26] Liu Y, Dai F, Dong L, Xu NW, Feng P. Experimental investigation on the fatigue mechanical properties of intermittently jointed rock models under cyclic uniaxial compression with different loading parameters. Rock Mech Rock Eng 2018; 51(1):47-68.

[27] Lavrov A. Fracture-induced physical phenomena and memory effects in rocks: A review. Strain 2005; 41(4):135-49.

[28] Meng QB, Chen YL, Zhang MW, Han LJ, Pu H, Liu JF. On the Kaiser effect of rock under cyclic loading and unloading conditions: Insights from acoustic emission monitoring. Energies 2019; 12(17):3255.

[29] Stavrakas I. Acoustic emissions and pressure stimulated currents experimental techniques used to verify Kaiser effect during compression tests of Dionysos marble. Frat Ed Integr Strutt 2017; 11(40):32-40.

[30] Mori Y, Obata Y, Pavelka J, Sikula J, Lokajicek T. AE Kaiser effect and electromagnetic emission in the deformation of rock sample. J Acoustic Emission 2004; 22:91-102.

[31] Varotsos PA, Sarlis NV, Skordas ES. Natural Time Analysis: The New View of Time: Precursory Seismic Electric Signals, Earthquakes and Other Complex Time Series. Heidelberg: Springer; 2011.

[32] Exadaktylos GE, Vardoulakis I, Kourkoulis SK. Influence of nonlinearity and double elasticity on flexure of rock beams. II. Characterization of Dionysos marble. Int J Solids Struct 2001; 38(22-23):4119-45.

[33] Vardoulakis I, Kourkoulis SK. Mechanical Properties of Dionysos Marble. Final Report of the European Union Environment Project EV5V-CT93-0300 ‘‘Monuments under Seismic Action”. Athens: National Technical University of Athens; 1997.

[34] Cai M. Practical estimates of tensile strength and Hoek-Brown strength parameter mi of brittle rocks. Rock Mech Rock Eng 2010; 43(2): 167-84.

[35] Atkinson BK, Meredith PG. Experimental fracture mechanics data for rocks and minerals. In: Fracture Mechanics of Rock. London: Academic Press Geology Series; 1987.p.477-519.

[36] Bandis S, Lumsden AC, Barton NR. Experimental studies of scale effects on the shear behaviour of rock joints. Int J Rock Mech Min Sci Geomech Abstr 1981; 18(1):1-21.

[37] Wang J, Ma FS. Method to address brittle rock strength scatter through fracture density. Rock Mech Rock Eng 2019; 52(9):3485-91.

[38] Liu DQ, He MC, Cai M. A damage model for modeling the complete stressstrain relations of brittle rocks under uniaxial compression. Int J Damage Mech 2018; 27(7):1000-19.

[39] Eberhardt E, Stead D, Stimpson B. Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 1999; 36(3):361-80.

[40] Li C, Nordlund E. Experimental verification of the Kaiser effect in rocks. Rock Mech Rock Eng 1993; 26(4):333-51.

[41] Kaiser J. Untersuchung über das Auftreten von Geräuschen beim Zugversuch. Doctoral dissertation. München: Universität München (TUM); 1950.

[42] Tanimoto K, Nakamura J, Fudo R. Application of acoustic emission in in-situ test. In:Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering. 1981.p.15-19.

[43] Lavrov A. Kaiser effect observation in brittle rock cyclically loaded with different loading rates. Mech Mater 2001; 33(11):669-77.

[44] Holcomb DJ. General theory of the Kaiser effect. Int J Rock Mech Min Sci Geomech Abstr 1993; 30(7):929-35.

[45] Vallianatos F, Triantis D. A non-extensive view of the pressure stimulated current relaxation during repeated abrupt uniaxial load-unload in rock samples. EPL Europhys Lett 2013; 104(6):68002.

[46] Varotsos PA, Skordas ES, Sarlis NV, Christopoulos SG. Review of the natural time analysis method and its applications. Mathematics 2024; 12(22):3582.

[47] Vallianatos F, Michas G, Benson P, Sammonds P. Natural time analysis of critical phenomena: The case of acoustic emissions in triaxially deformed Etna basalt. Phys A Stat Mech Appl 2013; 392(20):5172-8.

[48] Niccolini G, Potirakis SM, Lacidogna G, Borla O. Criticality hidden in acoustic emissions and in changing electrical resistance during fracture of rocks and cement-based materials. Materials 2020; 13(24):5608.

[49] Loukidis A, Pasiou ED, Sarlis NV, Triantis D. Fracture analysis of typical construction materials in natural time. Phys A Stat Mech Appl 2020; 547:123831.

[50] Loukidis A, Perez-Oregon J, Pasiou ED, Sarlis NV, Triantis D. Similarity of fluctuations in critical systems: Acoustic emissions observed before fracture. Phys A Stat Mech Appl 2021; 566:125622.

[51] Triantis D, Sarlis NV, Loukidis A, Pasiou ED, Stavrakas I, Kourkoulis SK. Criticality indices provided by the evolution of pressure stimulated currents and acoustic emissions in the natural time domain. Theor Appl Fract Mech 2023; 128:104115.

[52] Friedrich LF, Cezar ÉS, Colpo AB, Tanzi BNR, Sobczyk M, Lacidogna G, Niccolini G, Kosteski LE, Iturrioz I. Long-range correlations and natural time series analyses from acoustic emission signals. Appl Sci 2022; 12(4):1980.

[53] Uyeda S, Kamogawa M, Tanaka H. Analysis of electrical activity and seismicity in the natural time domain for the volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan. J Geophys Res Solid Earth 2009; 114(B2):B02310.