Uncertainty and universality in the power-law singularity as a precursor of catastrophic rupture

Jin, Yi; Xia, Mingji; Wang, Haiying

doi:10.1007/s11433-012-4727-4

Cited by 4 publications

(5 citation statements)

References 19 publications

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“…Thus, we have λ ≥ 2 (see Figure b). The result of λ = 2 (namely,

β_{F} = \frac{1}{λ} - 1 = - \frac{1}{2}

) can be derived in terms of series expansion (Jin et al, ). In series expansion, the first term of the series equals to zero due to energy criterion and the other order terms higher than the second one are omitted.…”

Section: Discussionmentioning

confidence: 99%

The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

et al. 2018

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The acceleration precursor of catastrophic rupture in rock‐like materials is usually characterized by a power law relationship, but the exponent exhibits a considerable scatter in practice. In this paper, based on experiments of granites and marbles under quasi‐static uniaxial and unconfined compression, it is shown that the power law exponent varies between −1 and −1/2. Such a changeable power law singularity can be justified by the energy criterion and a power function approximation. As the power law exponent is close to the lowest value of −1, rocks are prone to a perfect catastrophic rupture. Furthermore, it is found that the fitted reduced power law exponent decreases monotonically in the vicinity of a rupture point and converges to its lower limit. Therefore, the upper bound of catastrophic rupture time is constrained by the lowest value of the exponents and can be estimated in real time. This implies that, with the increase of real‐time sampling data, the predicted upper bound of catastrophic rupture time can be unceasingly improved.

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“…Thus, we have λ ≥ 2 (see Figure b). The result of λ = 2 (namely,

β_{F} = \frac{1}{λ} - 1 = - \frac{1}{2}

Section: Discussionmentioning

confidence: 99%

The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

et al. 2018

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“…In addition, the applied load P of cracking tests was selected as the controlling variable. Assuming that the controlling variable is continuous and derivable with the response variable, the applied load P can be expressed as the function of the damage factor D, that is, P(D), which can be given by the Taylor expansion (Jin et al, 2012;Liang et al, 2016):…”

Section: Damage Model For Catastrophic Failurementioning

confidence: 99%

“…In addition, the applied load P of cracking tests was selected as the controlling variable. Assuming that the controlling variable is continuous and derivable with the response variable, the applied load P can be expressed as the function of the damage factor D , that is, P ( D ), which can be given by the Taylor expansion (Jin et al., 2012; Liang et al., 2016):

P(D)={P}_{f}+{\left(\frac{dP}{dD}\right)}_{{D}_{f}}\left({D}_{f}-D\right)+\frac{1}{2}{\left(\frac{{d}^{2}P}{{d}^{2}D}\right)}_{{D}_{f}}{\left({D}_{f}-D\right)}^{2}+\mathcal{O}{\left({D}_{f}-D\right)}^{2}

where P f is the failure load, which equals the maximum load P max of the cracking test. It is worth noting that the terms with order higher than two were omitted.…”

Section: Introductionmentioning

confidence: 99%

Mode I Microscopic Cracking Process of Granite Considering the Criticality of Failure

Mo,

Zhao,

Zhang

2023

JGR Solid Earth

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Rock failure under tensile loading conditions is significant for rock engineering stability and underground energy development. However, a comprehensive understanding of the rock cracking process and the corresponding failure pattern at microscale remains unclear. Therefore, the cracking process and the damage evolution of rock and their underlying mechanisms were systematically investigated. In this study, the fracture behavior of granite was examined by performing mode I fracture tests. For extensive analysis of the cracking process, the cracks were captured in real‐time by scanning electron microscope, and the two fracture toughnesses of the double‐K model were evaluated. Subsequently, fracture morphologies of the post‐failure specimens were analyzed to further investigate the cracking mechanisms. The experimental results indicated the following: (a) the propagated direction of cracks was controlled by the fracture toughness of mineral grains and grain boundaries; and (b) the ratio of the two fracture toughnesses was correlated with fracture tortuosity. Furthermore, two damage modes of granite were found: catastrophic failure and non‐catastrophic failure modes. The former showed precursory behavior prior to catastrophic failure, while the latter did not. The underlying mechanisms of damage modes were revealed as follows: (a) the increased degree of heterogeneity caused by mineral composition complexity led to the early arrival of precursors; and (b) the occurrence of catastrophic or non‐catastrophic failure mode was determined by the difference in grain‐scale heterogeneity. Our results found at microscale also have implications for understanding the macroscopic failure process of rocks.

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“…Especially when b F ¼ À1 (i.e., ¼ 2), the rupture time can be determined by extrapolating the inverse rate R À1 to the abscissa (Boue´et al, 2015;Voight, 1988). However, the power-law singularity exponent b F is not always a constant in reported measurements but exhibits a large dispersion (Boue´et al, 2015;Cornelius and Scott, 1993;Hao et al, 2017;Jin et al, 2012;Kilburn, 2003;Voight and Cornelius, 1991;Xue et al, 2018). The uncertainty resulting from the scatter of the exponent makes it difficult to use such methods for prediction of the rupture time (Boue´et al, 2015;Hao et al, 2017;Xue et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Localization of deformation and its effects on power-law singularity preceding catastrophic rupture in rocks

Xue

Hao

Yang

et al. 2019

International Journal of Damage Mechanics

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Three distinct length scales are involved in the deformation evolution and catastrophic rupture of heterogeneous rocks in general: two essential ones are the specimen size macroscopically and the grain size at micro-scale respectively, the other is the emerging localized band of deformation and damage. The band initiates almost nearby the peak load, and the rupture eventually occurs afterwards within the localized band. In this paper, we report that with the evolution of concentrated high strain and damage in the localized band, a power-law singularity emerges within the localized band preceding the eventual rupture. The localization of deformation imposes a spatial non-uniqueness on the power-law singularity, and then leads to a trans-scale characteristic of the power-law singularity. Based on this characteristic, it is demonstrated that the singularity presented by the global response of a whole specimen comes from the singularity of local response in the localized band. The localization and the power-law singularity are associated precursory events, spatially and temporally, respectively, before macroscopic rupture. In particular, based on the power-law singularity exhibited in the zonal areas near or across the rupture surface, a prediction of the occurrence time of catastrophic rupture can be made accordingly. This provides a practically helpful approach to the prediction of rupture, merely by means of monitoring the zonal areas adjacent to the localized band.

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Uncertainty and universality in the power-law singularity as a precursor of catastrophic rupture

Cited by 4 publications

References 19 publications

The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

Mode I Microscopic Cracking Process of Granite Considering the Criticality of Failure

Localization of deformation and its effects on power-law singularity preceding catastrophic rupture in rocks

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