Anisotropic Damage Models for Geomaterials: Theoretical and Numerical Challenges

Xu, Hao; Arson, Chloé

doi:10.1142/s0219876213420073

Cited by 30 publications

(24 citation statements)

References 56 publications

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“…The Differential Stress Induced Damage (DSID) model (Xu and Arson, 2014) allows predicting mechanical anisotropy induced by a reorientation of stress principal directions in the rock mass (change of differential stress). CDM is used to predict the statistical average response of the cracked rock, without describing the real geometry of each micro-crack.…”

Section: Outline Of the Differential Stress Induced Damage Modelmentioning

confidence: 99%

“…The irreversible deformation due to damage follows an associated flow rule, which allows representing physical anisotropic trends of the deformation tensor during the damage process. More details are provided in (Xu and Arson, 2014). …”

Section: Outline Of the Differential Stress Induced Damage Modelmentioning

confidence: 99%

“…Continuum Damage Mechanics (CDM) provides a theoretical framework to relate geometrical fabric tensors to stiffness, and therefore, predict damaged rock mechanical properties (Colovos et al, 2013). In this paper, the DSID model recently proposed by the authors (Xu and Arson, 2014) is used to simulate fracture propagation around a pressurized borehole with the Finite Element Method (FEM). Due to the complexity of the model verification, comparison of the DSID model predictions against experimental data is not presented in this paper: calibration and verification will be studied in future work.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale Discontinuities Due to Differential Stress around a Pressurized Borehole

Arson

Busetti

2014

Geo-Congress 2014 Technical Papers

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Most fracture propagation models do not properly represent smaller-scale discontinuities in the process zone. This paper reviews the different modeling strategies available to date to model crack propagation at microscopic, mesoscopic and macroscopic scales. The Differential Stress Induced Damage (DSID) model recently proposed by the authors (Xu and Arson, 2014) is then used to simulate fracture propagation around a pressurized borehole with the Finite Element Method. In a pristine rock mass, the damage zone presents several symmetries in three dimensions, which are in agreement with the definition of the damage-driving force controlling the initiation and propagation of damage. If hydraulic fracturing is enhanced by the presence of initial cracks, the propagation of the damage zone depends on the geometry of the initial defects. It is found that simulating rock initial texture by a smeared damaged zone provides good analogs to the viscosity-dominated and toughness-dominated fracture propagation regimes expected during hydraulic fracturing. Future work will be dedicated to the fully coupled formulation of a hydro-mechanical model of damage around hydraulic fractures.

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Section: Outline Of the Differential Stress Induced Damage Modelmentioning

confidence: 99%

Section: Outline Of the Differential Stress Induced Damage Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiscale Discontinuities Due to Differential Stress around a Pressurized Borehole

Arson

Busetti

2014

Geo-Congress 2014 Technical Papers

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“…In non‐elastic continua, models require that the maximum size of the plastic or damage zone near the fracture tip be smaller than the specimen or domain dimensions by at least two orders of magnitude. In continuum damage mechanics (CDM), models were either based on phenomenology or grounded on micromechanics . At the scale of the representative elementary volume (REV), CDM models were proposed to account for unilateral effects , microcrack friction and strength difference in tension and compression .…”

Section: Introductionmentioning

confidence: 99%

“…In the following study, we propose a numerical method that couples a CDM model (for the bulk) to a cohesive zone model (for the fracture), in order to simulate the propagation of a discrete mode II fracture within a damaged zone. In Section 2, we provide an analysis of the dissipation processes that are represented during crack propagation in the CZM and in the CDM differential stress induced damage (DSID) model . Then we calibrate the CZM/CDM model so as to reproduce the stress/strain curves of Bakken shale during typical triaxial compression tests.…”

Section: Introductionmentioning

confidence: 99%

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

Jin

Arson

et al. 2016

Num Anal Meth Geomechanics

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Summary We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.

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Integration of a continuum damage model for shale with the cutting plane algorithm

Prévost

2016

Int. J. Numer. Anal. Meth. Geomech.

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The stability of integration is essential to numerical simulations especially when solving nonlinear problems. In this work, a continuum damage mechanics model proposed by the first author is implemented with an integration method named cutting plane algorithm (CPA) to improve the robustness of the simulation. This integration method is one type of return mapping algorithm that bypasses the need for computing the gradients. We compare the current integration method with the previous direct method, and the result shows that the cutting plane algorithm exhibits excellent performance under large loading rate conditions. To enhance accuracy of the new method, a control procedure is utilized in the implementation of the algorithm based on error analysis. Thereafter, the theory of poromechanics is utilized with the damage model to account for the effects of fluid diffusion. Laboratory tests simulated with finite element method illustrate distinct behaviors of shale with different loading rates and indicate the development of microcrack propagation under triaxial compression. Error analysis.The error has been investigated on the stress changing for the same deviatoric strain loading. The test result with large strain is compared with the convergent test. The normalized

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Anisotropic Damage Models for Geomaterials: Theoretical and Numerical Challenges

Cited by 30 publications

References 56 publications

Multiscale Discontinuities Due to Differential Stress around a Pressurized Borehole

Multiscale Discontinuities Due to Differential Stress around a Pressurized Borehole

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

Integration of a continuum damage model for shale with the cutting plane algorithm

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