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A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults

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  • Carpinteri, Alberto
  • Paggi, Marco

Abstract

Experimental results indicate that large faults involved in earthquakes possess low strength, low friction coefficient and high fracture energy, in comparison with data obtained according to small scale laboratory tests on the same material. The reasons for such an unexpected anomalous behaviour have been the subject of several researches in the past and are still under debate in the Scientific Community. In this note, we propose a unifying interpretation of these size-scale effects according to fractal geometry, which represents the proper mathematical framework for the analysis of the multi-scale properties of rough surfaces in contact. This contribution sheds a new light on the non-linear properties of friction and on the understanding the fundamental physics governing the scaling of the mechanical properties in geophysics from the laboratory to a planetary scale.

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  • Carpinteri, Alberto & Paggi, Marco, 2009. "A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 540-546.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:2:p:540-546
    DOI: 10.1016/j.chaos.2007.01.075
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    References listed on IDEAS

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    1. Judith S. Chester & Frederick M. Chester & Andreas K. Kronenberg, 2005. "Fracture surface energy of the Punchbowl fault, San Andreas system," Nature, Nature, vol. 437(7055), pages 133-136, September.
    2. Sahimi, Muhammad & Robertson, Michelle C. & Sammis, Charles G., 1992. "Relation between the earthquake statistics and fault patterns, and fractals and percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 57-68.
    3. Giulio Di Toro & Stefan Nielsen & Giorgio Pennacchioni, 2005. "Earthquake rupture dynamics frozen in exhumed ancient faults," Nature, Nature, vol. 436(7053), pages 1009-1012, August.
    4. Chakrabarti, Bikas K & Stinchcombe, Robin B, 1999. "Stick-slip statistics for two fractal surfaces: a model for earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 27-34.
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    Cited by:

    1. Paggi, Marco & Carpinteri, Alberto, 2009. "Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1136-1145.
    2. Carpinteri, Alberto & Lacidogna, Giuseppe & Puzzi, Simone, 2009. "From criticality to final collapse: Evolution of the “b-value” from 1.5 to 1.0," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 843-853.
    3. Carpinteri, A. & Lacidogna, G. & Niccolini, G., 2009. "Fractal analysis of damage detected in concrete structural elements under loading," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2047-2056.
    4. Zengchao, Feng & Yangsheng, Zhao & Dong, Zhao, 2009. "Investigating the scale effects in strength of fractured rock mass," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2377-2386.

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