Mechanistic Analysis of Rock Damage Anisotropy and Rotation Around Circular Cavities

Xu, Hao; Arson, Chloé

doi:10.1007/s00603-014-0707-5

Cited by 12 publications

(11 citation statements)

References 54 publications

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“…The proposed discrete damage model provides a detailed description of the fabric of materials damaged in compression with only 3 damage parameters (, k c , c ), 2 initial crack parameters (a 0 and N ) and 2 elasticity parameters (E 0 and 0 ). This is a significant gain of information compared to former damage models implemented in FEM, which are formulated using a second-order damage tensor at most (Jin et al, 2017;Xu and Arson, 2015).…”

Section: Elasticitymentioning

confidence: 99%

Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications

Jin

Arson

2017

International Journal of Damage Mechanics

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The discrete damage model presented in this paper accounts for 42 non-interacting crack microplanes directions. At the scale of the representative volume element, the free enthalpy is the sum of the elastic energy stored in the non-damaged bulk material and in the displacement jumps at crack faces. Closed cracks propagate in the pure mode II, whereas open cracks propagate in the mixed mode (I/II). The elastic domain is at the intersection of the yield surfaces of the activated crack families, and thus describes a non-smooth surface. In order to solve for the 42 crack densities, a Closest Point Projection algorithm is adopted locally. The representative volume element inelastic strain is calculated iteratively using the Newton–Raphson method. The proposed damage model was rigorously calibrated for both compressive and tensile stress paths. Finite element method simulations of triaxial compression tests showed that the transition between brittle and ductile behavior at increasing confining pressure can be captured. The cracks’ density, orientation, and location predicted in the simulations are in agreement with experimental observations made during compression and tension tests, and accurately show the difference between tensile and compressive strength. Plane stress tension tests simulated for a fiber-reinforced brittle material also demonstrated that the model can be used to interpret crack patterns, design composite structures and recommend reparation techniques for structural elements subjected to multiple damage mechanisms.

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Section: Elasticitymentioning

confidence: 99%

Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications

Jin

Arson

2017

International Journal of Damage Mechanics

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“…However, according to our implementation experience, it works well in all cases. The cutting plane algorithm replaces the previous direct method and solves the nonlinear equations for the stress–strain relationship. Comparing the results between the two methods, we obtain that the same answer that proves the cutting plane algorithm is implemented correctly.…”

Section: Constitutive Model and Implementationmentioning

confidence: 99%

“…Comparing the results between the two methods, we obtain that the same answer that proves the cutting plane algorithm is implemented correctly. The disadvantage of the direct method in our previous version is that when the number of loading steps is decreased (i.e., the size of the loading rate is increased), the computation is not convergent, or infinite loop may happen during iterations. These unstable issues have been resolved by the cutting plane algorithm.…”

Section: Constitutive Model and Implementationmentioning

confidence: 99%

“…However, to implement a non‐linear constitutive model for a material in FEM is always a challenge. Isotropic and anisotropic damage models proposed by different authors are many , but successful implementations in FEM, especially with anisotropic damage, are rare . The integration method used in solving nonlinear stress–strain history of materials is commonly proposed for plasticity or viscoplasticity .…”

Section: Introductionmentioning

confidence: 99%

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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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“…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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Mechanistic Analysis of Rock Damage Anisotropy and Rotation Around Circular Cavities

Cited by 12 publications

References 54 publications

Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications

Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications

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

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

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