A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Levasseur, Séverine; Collin, Frèdèric; Charlier, Robert; Kondo, Djimédo

doi:10.1016/j.engfracmech.2011.03.009

Cited by 14 publications

(6 citation statements)

References 24 publications

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“…Micro-mechanical damage models (Pensée et al, 2002;Dormieux et al, 2006;Zhu et al, 2007;Levasseur et al, 2011) Kachanov (1992) as:…”

Section: Micro-mechanical Modelsmentioning

confidence: 99%

Bayesian paradigm to assess rock compression damage models

Arson¹,

Medina-Cetina²

2015

Environmental Geotechnics

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Energy extraction and waste storage in geological formations raise interest in developing systematic and reliable calibration methods to assess rock models performance. A methodology is proposed to improve damage prediction in sandstone, based on Finite Element simulations coupled with the Bayesian paradigm. To illustrate this methodology, parameters of a Continuum Damage Mechanics model are defined as random variables. (1) First, probability density functions are formulated for each parameter (expert's judgement) and sampled later independently to simulate likely random sandstone responses during a triaxial compression test (forward problem). (2) Second, experimental data is introduced (new evidence available), which allows updating the probability distributions depicting the model parameters (inverse problem). Results show that it is possible to quantify the impact of experimental evidence into the rock characterization, and that correlations between all rock damage parameters can be retrieved. Mechanically speaking this means that: (a) similar accuracy in the prediction of damage might be achievable with less model parameters, (b) and the input of energy released to initiate crack propagation is contingent upon conditions external to the model (e.g., initial texture of the rock). Results from this investigation provide promising applications of the probabilistic calibration approach to damage models in multi-phase porous media.

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“…Micro-mechanical damage models (Pensée et al, 2002;Dormieux et al, 2006;Zhu et al, 2007;Levasseur et al, 2011) Kachanov (1992) as:…”

Section: Micro-mechanical Modelsmentioning

confidence: 99%

Bayesian paradigm to assess rock compression damage models

Arson¹,

Medina-Cetina²

2015

Environmental Geotechnics

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“…Micro-mechanical damage models [22,54] assume that the rock Representative Element Volume (REV) is populated with a given distribution of cracks characterized by a specific shape (usually, spherical, penny-shaped or ellipsoidal cracks). Assumptions on the shape and density of cracks allow to express explicitly the strain concentration tensor, and further, to derive the theoretical expression of the Helmholtz free energy of the rock solid skeleton.…”

Section: Thermo-mechanical Damage Models For Rock: Continuum Damage M...mentioning

confidence: 99%

A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure

Zhu

Arson

2013

Acta Geotech.

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A thermodynamic framework is proposed to couple the effect of mechanical stress and temperature on crack opening and closure in rocks. The model is based on Continuum Damage Mechanics, with damage defined as the secondorder crack density tensor. The free energy of the damaged rock is expressed as a function of deformation, temperature and damage. The damage criterion captures mode I crack propagation, the reduction of toughness due to heating, and the increase of energy release rate with cumulated damage. Crack closure is modeled through unilateral effects produced on rock stiffness. The model was calibrated and verified against published experimental data. Thermo-mechanical crack opening (resp. closure) was studied by simulating a triaxial compression test (resp. uniaxial extension test ) including a thermal loading phase. The degradation of stiffness due to tensile stress and recovery of stiffness induced by both mechanical and thermo-mechanical unilateral effects are well captured. The thermo-mechanical energy release rate increases with thermal dilation, and also decreases with ambient temperature. It was observed that there is a temperature threshold, below which the rock behaves elastically. A parametric study also showed that the model can capture hardening and softening during thermo-mechanical closure (for specific sets of parameters). These numerical observations may guide the choice of rock material used in geotechnical design, especially for nuclear waste disposals or compressed air storage facilities.

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“…First, the mathematical framework used in this study is constructed on the basis of thermodynamic energy change. This framework is based on Murakami and Kamiya [1997], who used a materials science approach, which generally includes a framework based on energy change and employs variables that describe changes from the initial state [ Levasseur et al , 2011]. The whole system is regarded as isotropic and homogeneous at the initial state with this idea.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting

Suzuki

2012

J. Geophys. Res.

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[1] The importance of the damage effect on dynamic earthquake slip behavior is clarified using the damage tensor variable. Dynamic mode II faults that are embedded in damage-inducing media are assumed to relate to damage effects. This study confirms that the rupture velocity for spontaneous fault tip growth in the damage medium is reduced, being slightly smaller than rupture velocities observed for classical elastic material. Inelastic energy loss resulting in damage is relatively small but nonnegligible to the accumulated fracture energy. Two framework parameters employed in this study determine microcrack orientations and modes of microcracks and provide information on deviations in microcrack distribution between isotropic and nonisotropic ones. Spatial microcrack distribution patterns in isotropic and homogeneous systems are strongly dependent on a parameter related to the damage creation criterion. When considering secondary faulting, two apparently different behaviors, pulverization and branch development, are understood in a single framework, which gives a new insight into fault zone formation. The present results show that damage effect must be treated as a tensor variable rather than a scalar one as employed in many previous studies.Citation: Suzuki, T. (2012), Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting,

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A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Cited by 14 publications

References 24 publications

Bayesian paradigm to assess rock compression damage models

Bayesian paradigm to assess rock compression damage models

A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure

Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting

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