Percolation and fracture

Chélidzé, T.

doi:10.1016/0031-9201(82)90075-9

Cited by 103 publications

(53 citation statements)

References 9 publications

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“…As an analogy to the study of critical phase transitions in statistical physics, it has been argued that the fracture of heterogeneous materials could be viewed as a critical phenomenon either at the laboratory scale or at the geophysical scale (Chelidze, 1982;Allegre et al, 1982;Sornette and Sornette, 1990;Herrmann and Roux, 1990;Sornette and Sammis, 1995;Sornette and Andersen, 1998;Bowman et al, 1998;Kossobokov et al, 1999;Sornette, 2000;Moreno, 2000;Gluzman and Sornette, 2001;Guarino et al, 2002;Rundle et al, 2003, and references therein). We note that other researchers have associated brittle rupture with a firstorder phase transition (Buchel and Sethna, 1997;Kun and Herrmann, 1999;Rundle et al, 2003, and references therein).…”

Section: Focus On Mhz Em Fieldmentioning

confidence: 99%

On the puzzling feature of the silence of precursory electromagnetic emissions

Eftaxias

Potirakis

Chélidzé

2013

Nat. Hazards Earth Syst. Sci.

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Abstract. It has been suggested that fracture-induced MHzkHz electromagnetic emissions (EME), which emerge from a few days up to a few hours before the main seismic shock occurrence permit a real-time monitoring of the damage process during the last stages of earthquake preparation, as it happens at the laboratory scale. Despite fairly abundant evidence, electromagnetic (EM) precursors have not been adequately accepted as credible physical phenomena. These negative views are enhanced by the fact that certain "puzzling features" are repetitively observed in candidate fractureinduced pre-seismic EME. More precisely, EM silence in all frequency bands appears before the main seismic shock occurrence, as well as during the aftershock period. Actually, the view that "acceptance of "precursive" EM signals without convincing co-seismic signals should not be expected" seems to be reasonable. In this work we focus on this point. We examine whether the aforementioned features of EM silence are really puzzling ones or, instead, reflect well-documented characteristic features of the fracture process, in terms of universal structural patterns of the fracture process, recent laboratory experiments, numerical and theoretical studies of fracture dynamics, critical phenomena, percolation theory, and micromechanics of granular materials. Our analysis shows that these features should not be considered puzzling.

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Section: Focus On Mhz Em Fieldmentioning

confidence: 99%

On the puzzling feature of the silence of precursory electromagnetic emissions

Eftaxias

Potirakis

Chélidzé

2013

Nat. Hazards Earth Syst. Sci.

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“…In analogy to the study of critical phase transitions in statistical physics, it has been recently argued that the fracture of heterogeneous materials could be viewed as a critical phenomenon (Herrmann and Roux, 1990;Vanneste and Sornette, 1992;Lamaignere et al, 1996;Andersen et al, 1997;Sornette, 2000), either at laboratory scale (Petri et al, 1994;Guarino et al, 1998Guarino et al, , 2002 or at geophysical scales (Chelidze, 1982;Allegre et al, 1982;Sornette and Sornette, 1990;Diodati et al, 1991;Sornette and Sammis, 1995;Saleur et al, 1996a,b;Main, 1996;Bowman et al, 1998;Kossobokov et al, 1999). This result comes from different observations including power law scaling in space (fractals), time and energy, long-range correlations, or the divergence of the rate of energy dissipation near the critical point.…”

Section: Introductionmentioning

confidence: 99%

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

Kapiris

Eftaxias

Νομικός

et al. 2003

Nonlin. Processes Geophys.

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Abstract. In analogy to the study of critical phase transitions in statistical physics, it has been argued recently that the fracture of heterogeneous materials could be viewed as a critical phenomenon, either at laboratory or at geophysical scales. If the picture of the development of the fracture is correct one may guess that the precursors may reveal the critical approach of the main-shock. When a heterogeneous material is stretched, its evolution towards breaking is characterized by the appearance of microcracks before the final break-up. Microcracks produce both acoustic and electromagnetic (EM) emission in the frequency range from VLF to VHF. The microcracks and the associated acoustic and EM activities constitute the so-called precursors of general fracture. These precursors are detectable not only at laboratory but also at geophysical scales. VLF and VHF acoustic and EM emissions have been reported resulting from volcanic and seismic activities in various geologically distinct regions of the world. In the present work we attempt to establish the hypothesis that the evolution of the Earth's crust towards the critical point takes place not only in a mechanical but also in an electromagnetic sense. In other words, we focus on the possible electromagnetic criticality, which is reached while the catastrophic rupture in the Earth's crust approaches. Our main tool is the monitoring of micro-fractures that occur before the final breakup, by recording their radioelectromagnetic emissions. We show that the spectral power law analysis of the electromagnetic precursors reveals distinguishing signatures of underlying critical dynamics, such as: (i) the emergence of memory effects; (ii) the decrease with time of the anti-persistence behaviour; (iii) the presence of persistence properties in the tail of the sequence of the precursors; and (iv) the acceleration of the precursory electromagnetic energy release. Moreover, the statistical analysis of the amplitudes of the electromagnetic fluctuations reveals the breaking of the symmetry as the theory predicts. Finally, we try to answer the question: how universal the observed Correspondence to: K. A. Eftaxias (ceftax@phys.uoa.gr) electromagnetic critical behaviour of the failing system is?

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“…Faults are generated by large-scale tectonic events, and joints by uplift and erosion, excess fluid pressures, and ther- Largely because of data uncertainty, and lack of distinction between faults and joints, there has been considerable debate whether available fracture network measurements, and understanding of fracturing mechanisms, suggest fractures in the Earth to be well above the percolation threshold, and highly interconnected [Barton, 1995], or, conversely, near the percolation threshold and thus poorly connected [Chelidze, 1982;Madden, 1983 With the length distribution being fixed, we examine the critical percolation parameter, P•, which we define as the threshold at which a network has a connection probability across the domain of 0.5. Standard percolation theory concepts hold only for random placements of constant length bonds, or for distributions of bond lengths which are significantly smaller than the domain size.…”

Section: Introductionmentioning

confidence: 99%