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Fractal analysis of damage detected in concrete structural elements under loading

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  • Carpinteri, A.
  • Lacidogna, G.
  • Niccolini, G.

Abstract

In Civil Engineering materials subjected to stress or strain states a quantitative evaluation of damage is of great importance due to the critical character of this phenomenon, which at a certain point suddenly turns into a catastrophic failure. An effective damage assessment criterion is represented by the statistical analysis of the amplitude distribution of acoustic emission (AE) signals emerging from the growing microcracks. The amplitudes of such signals are distributed according to the Gutenberg–Richter (GR) law and characterised through the b-value which decreases systematically with damage growth. On the other hand, the damage process is also characterised by the progressive coalescence of microcracks to form fracture surfaces. Geometrically the fractal dimension D of the damaged domain is expected to decrease from an initial value comprised between 2 and 3 towards a final value nearly equal to 2. The b-value and the fractal analysis, are here applied to two case studies of concrete specimens loaded up to failure, and the obtained results are compared and discussed. In particular, we emphasize that a single fractal dimension does not adequately describe a crack network, since two damaged domains with the same fractal dimension could have significantly different properties.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2047-2056
    DOI: 10.1016/j.chaos.2009.03.165
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Carpinteri, Alberto & Pugno, Nicola & Puzzi, Simone, 2009. "Strength vs. toughness optimization of microstructured composites," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1210-1223.
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    Cited by:

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    2. Weiguang Ren & Chaosheng Wang & Yang Zhao & Dongjie Xue, 2023. "Research on Precursor Information of Brittle Rock Failure through Acoustic Emission," Mathematics, MDPI, vol. 11(19), pages 1-16, October.
    3. Song, Honghua & Zhao, Yixin & Elsworth, Derek & Jiang, Yaodong & Wang, Jiehao, 2020. "Anisotropy of acoustic emission in coal under the uniaxial loading condition," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Yang, Yang & Bashir, Musa & Michailides, Constantine & Mei, Xuan & Wang, Jin & Li, Chun, 2021. "Coupled analysis of a 10 MW multi-body floating offshore wind turbine subjected to tendon failures," Renewable Energy, Elsevier, vol. 176(C), pages 89-105.
    5. Dongxu Liang & Nong Zhang & Lixiang Xie & Guangming Zhao & Deyu Qian, 2019. "Damage and fractal evolution trends of sandstones under constant-amplitude and tiered cyclic loading and unloading based on acoustic emission," International Journal of Distributed Sensor Networks, , vol. 15(7), pages 15501477198, July.
    6. da Silva, Sérgio Luiz E.F., 2021. "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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