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Experimental and Numerical Investigation of the Catastrophic Stage of Failure on Different Scales from Rock Sample to Coal Mine

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Abstract

Doppler laser interferometry is used to measure the transient time between the slow quasi-stationary stage of damage accumulation in rock samples to the ultrafast catastrophic stage of failure as well as the duration of the autocatalytic stage of macroscopic fracture. Small rock samples are tested for compression and three-point bending, and the velocity of displacement of their lateral surfaces is measured up to macroscopic fracture. The surface velocity at the catastrophic stage proves to be three orders of magnitude higher than the average surface velocity at the quasi-stationary stage of damage accumulation. The transient time to catastrophic failure is estimated at 60–100 ms, and the duration of the ultrafast catastrophic failure stage is 15–20 ms for small marble samples. The transient stage is the process of self-organization of individual acts of fracture into the state of self-organized criticality. At this stage, the distribution of individual acts of fracture evolves into power-law distributions. A simple fracture model with power laws is proposed, which is in full agreement with the experimental data. The developed mathematical model is used to calculate fracture of small rock samples, reproducing uniaxial compression and three-point bending tests, as well as fracture in rock masses with mine openings. We also model the process of faulting and fracturing in the mountains of Central Altai, including the foreshock process, main event (the Chuya earthquake of September 27, 2003) and aftershock process. The calculated seismic process fully corresponds to the Gutenberg–Richter recurrence law, and the calculated aftershock process conforms to the Omori law.

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Funding

This work was supported by the Russian Science Foundation, project 19-17-00122.

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Authors and Affiliations

  1. National Research Tomsk State University, 634050, Tomsk, Russia

    P. V. Makarov, I. Yu. Smolin, A. Yu. Peryshkin, A. S. Kulkov & R. A. Bakeev

  2. Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, 634055, Tomsk, Russia

    P. V. Makarov, I. Yu. Smolin, A. Yu. Peryshkin, A. S. Kulkov & R. A. Bakeev

Authors
  1. P. V. Makarov
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  2. I. Yu. Smolin
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  3. A. Yu. Peryshkin
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  4. A. S. Kulkov
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  5. R. A. Bakeev
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Correspondence to P. V. Makarov.

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Translated from in Fizicheskaya Mezomekhanika, 2020, Vol. 23, No. 5, pp. 43–55.

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Makarov, P.V., Smolin, I.Y., Peryshkin, A.Y. et al. Experimental and Numerical Investigation of the Catastrophic Stage of Failure on Different Scales from Rock Sample to Coal Mine. Phys Mesomech 24, 155–165 (2021). https://doi.org/10.1134/S1029959921020053

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