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Avalanches in Functional Materials and Geophysics pp 77–97Cite as

Crackling Noise in Digital and Real Rocks–Implications for Forecasting Catastrophic Failure in Porous Granular Media

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Part of the book series: Understanding Complex Systems ((UCS))

Abstract

‘Crackling noise’ occurs in a wide variety of systems that respond to steady-state external forcing in an intermittent way, leading to sudden bursts of energy release similar to those heard when crumpling a piece of paper or listening to a fire. In rock physics sudden changes in internal stress associated with microscopically-brittle rupture events lead to acoustic emissions that can be recorded on the sample boundary, and used to infer the state of internal damage. Crackling noise is inherently stochastic, but the population of events often exhibits remarkably robust scaling properties, in terms of the source area, duration, energy, and in the waiting time between events. Here we describe how these scaling properties emerge and evolve spontaneously in a fully-dynamic discrete element model of sedimentary rocks subject to uniaxial compression applied at a constant strain rate. The discrete elements have structural disorder similar to that of a real rock, and this is the only source of heterogeneity. Despite the stationary strain rate applied and the lack of any time-dependent weakening processes, the results are all characterized by emergent power law distributions over a broad range of scales, in agreement with experimental observation. As deformation evolves, the scaling exponents change systematically in a way that is similar to the evolution of damage in experiments on real sedimentary rocks . The potential for real-time forecasting of catastrophic failure obeying such scaling rules is then examined by using synthetic and real data from laboratory tests and prior to volcanic eruptions. The combination of non-linearity in the constitutive rules and an irreducible stochastic component governed by the material heterogeneity and finite sampling of AE data leads to significant variations in the precision and accuracy of the forecast failure time. This leads to significant proportion of ‘false alarms’ (forecast too early) and ‘missed events’ (forecast too late), as well as an over-optimistic assessments of forecasting power and quality when the failure time is known (the ‘benefit of hindsight’). The evolution becomes progressively more complex, and the forecasting power diminishes, in going from ideal synthetics to controlled laboratory tests to open natural systems at larger scales in space and time.

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Acknowledgments

The bulk of this paper is based on the Néel lecture delivered by IGM at the 2014 European Union of Geosciences meeting in Vienna, and a shortened version delivered to the ‘Avalanches in Functional Materials and Geophysics’ meeting in Cambridge the same year. FK and AFB made significant material contributions to the presentations, and to the writing of this paper. IGM is grateful to Philip Meredith for many insights into rock physics that motivated the work described in the paper, as well as the many co-authors cited in the reference list, especially Jeremie Vasseur whose experimental results are reproduced in Fig. 5.7. Much of the work described in this paper was supported by the European Commission via the Complexity-NET pilot project ‘LOCAT’ and by the NERC project ‘EFFORT’, NE/H02297X/1.

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Authors and Affiliations

  1. School of Geoscience, Grant Institute, University of Edinburgh, James Hutton Road, Edinburgh, EH9 3FE, UK

    Ian G. Main & Andrew F. Bell

  2. Department of Theoretical Physics, University of Debrecen, P.O. Box 5, Debrecen, 4010, Hungary

    Ferenc Kun

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  1. Ian G. Main
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  2. Ferenc Kun
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Correspondence to Ian G. Main .

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Editors and Affiliations

  1. Department of Earth Sciences, University of Cambridge , Cambridge, United Kingdom

    Ekhard K.H. Salje

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

    Avadh Saxena

  3. Estructura i Constitutents de la Matèria, Universitat de Barcelona, Barcelona, Spain

    Antoni Planes

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Main, I.G., Kun, F., Bell, A.F. (2017). Crackling Noise in Digital and Real Rocks–Implications for Forecasting Catastrophic Failure in Porous Granular Media. In: Salje, E., Saxena, A., Planes, A. (eds) Avalanches in Functional Materials and Geophysics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-45612-6_5

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