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School of Civil and Environmental Engineering

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College of Engineering

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Georgia Water Resources Institute

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Georgia Transportation Institute

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Environmental Microbial Genomics Laboratory

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Now showing 1 - 9 of 9

Fracture-Induced Anisotropy of the Stress-Strain Response of Shale at Multiple Scales

(Georgia Institute of Technology, 2016) Xu, Hao ; Busetti, Seth ; Arson, Chloé

This paper investigates deformation and stiffness anisotropy induced by damage propagation in rock brittle deformation regime. Specifically, a Finite Element-based Continuum Damage Mechanics model is used to capture sample size effects and the influence of intrinsic anisotropy on the stress-strain response of shale. The Differential Stress Induced Damage (DSID) model previously proposed by the authors is calibrated against triaxial compression tests performed on North Dakota Bakken shale samples. Laboratory tests simulated with the Finite Element Method reproduce deformation and damage localization phenomena, and capture the increase of boundary effects expected in larger samples. Simulations performed for various initial states of damage are used to investigate the role of the dominant fabric anisotropy of the rock: bedding planes in shale are modeled by a smeared damage zone with the DSID model and by a discrete crack plane. The continuum approach successfully captures the development of microcrack propagation and energy dissipation at the early stage of the strain hardening process observed in triaxial compression tests. Additionally, using initial anisotropic damage can effectively account for various types of mechanical anisotropy in shale.
Probabilistic Optimization of a Continuum Mechanics Model to Predict Differential Stress-Induced Damage in Claystone

(Georgia Institute of Technology, 2014-06) Bakhtiary, Esmaeel ; Xu, Hao ; Arson, Chloé

Phenomenological modeling of anisotropic damage in rock raises many fundamental thermodynamic and mechanical issues. In this paper, the maximum likelihood method is used to analyze the performance of the Differential Stress Induced Damage (DSID) model recently formulated by Xu and Arson. The stress/strain relationship is a nonlinear function of parameters ncluding unknown constants (i.e.,damage constitutive parameters) and known variables (e.g., elastic parameters and controlled stress state). Logarithmic transformation, normalization and forward deletion are employed, in order to find the optimum number of constitutive parameters, as a trade off between accuracy and simplicity. For Eastern France claystone subject to deviatoric stress loading (e.g., triaxial and proportional compression loading), it is found that (1) only one damage parameter (a₂) is needed in the expression of the free energy to predict stress/strain curves; (2) a₂ controls the deviation of the current principal directions of stress to the principal directions of damage; (3) model parameters involved in the damage criterion can be related to a₂. As a result, a₂ is the only parameter needed to model differential-stress induced damage in Eastern France claystone. It is also shown that within the set of assumptions made in this study, the DSID model is not sensitive to the initial damage threshold C₀, except for C₀>10⁶ Pa a range of values in which only one constitutive parameter becomes insufficient to predict the stress/strain curves of damaged claystone. Coupling probabilistic calibration and optimization methods to numerical codes promises to allow adapting the complexity of anisotropic damage models to different rocks and stress paths.
Multi-scale Discontinuities Due to Differential Stress Around a Pressurized Borehole

(Georgia Institute of Technology, 2014-02) Xu, Hao ; Arson, Chloé ; Busetti, Seth

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 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.
Anisotropic Damage Models for Geomaterials: Theoretical and Numerical Challenges

(Georgia Institute of Technology, 2013-08) Xu, Hao ; Arson, Chloé

A new anisotropic damage model for rock is formulated and discussed. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. Drucker–Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Positivity of dissipation is ensured by using a nonassociate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Simulations show that the model meets thermodynamic requirements, follows a rigorous formulation, and predicts expected trends for damage, deformation and stiffness.
Modeling Damage Induced by Deviatoric Stress in Rock: Theoretical Framework

(Georgia Institute of Technology, 2013-07) Xu, Hao ; Arson, Chloé

This work focuses on the development of a new anisotropic damage model for porous rocks. This damage model is formulated within the framework of thermodynamic irreversible processes. Flow rules are expressed with the energy release rate conjugate to damage, as opposed to stress in most rock damage models. The damage criterion is chosen so as to distinguish between tension and compression strength. Non-elastic deformation due to damage is computed by an associate flow rule to capture the development of crack-induced strains in the main directions of damage. Preliminary numerical results illustrate the potential for a crack to propagate under hydraulic pressure. This research work is expected to link damage mechanics with fracture propagation, for possible applications of hydraulic fracturing at reservoir scale.
Modeling Stiffness Anisotropy Induced by Crack Opening in Rocks Subjected to Thermal versus Mechanical Stress Gradients

(Georgia Institute of Technology, 2013-06) Zhu, Cheng ; Arson, Chloé ; Xu, Hao

A thermodynamic framework is proposed to model the coupled effects of mechanical and thermal stresses in rocks. The model is based on Continuum Damage Mechanics with damage defined as the second-order crack density tensor. The free energy of damaged rock is expressed as a function of deformation, temperature, and damage. The damage criterion controls mode I crack propagation, captures temperature-induced decrease of rock toughness, and accounts for the increase of energy release rate necessary to propagate cracks in a damaged medium. Two loading paths have been simulated: (1) increase of ambient temperature followed by a triaxial compression test, (2) triaxial compression test followed by a confined heating phase. Results show that: (1) under anisotropic mechanical boundary conditions, heating produces damage, (2) higher temperature induces larger damage and deformation, (3) degradation of rock toughness due to an increase in temperature affects the damage threshold. The proposed framework is expected to bring new insights in the design and reliability assessment of geotechnical reservoirs and repositories, such as nuclear waste disposals, geothermal systems, carbon dioxide sequestration systems, and high-pressure gas reservoirs.
Modeling the Anisotropic Damaged Zone Around Hydraulic Fractures: Thermodynamic Framework and Simulation of Mechanical Tests

(Georgia Institute of Technology, 2013-06) Xu, Hao ; Arson, Chloé ; Busetti, Seth

We model crack propagation and damage induced by deviatoric stress around the crack tip. A new damage model is proposed to describe the damaged zone near fractures, in order to predict the mesoscale geomechanical behavior of rock during hydraulic fracturing. The process of new damage development follows a thermodynamic framework. An associated flow rule is utilized for irreversible strain rate while a non-associated flow rule is applied for damage evolution. Uniaxial tension and triaxial compression tests are simulated at the Gauss point of one element in MATLAB with the new damage model. The results illustrate the influence of anisotropic damage on stiffness degradation and residual strain development. The implementation of this new damage model in the commercial FEM software ABAQUS is undergoing. A preliminary Brazilian tension test is computed for the elastic domain using ABAQUS’ UMAT subroutine. The result agrees well with the analytic solution. The new damage model for rock matches the theoretical expectations, and shows that the proposed model can predict anisotropic damage.
On The Definition Of Damage In Time-Dependent Healing Models For Salt Rock

(Georgia Institute of Technology, 2012-07) Arson, Chloé ; Xu, Hao ; Chester, Fred M.

his research is motivated by the increasing need for geostorage facilities such as nuclear waste disposals, high-pressure gas reservoirs and carbon dioxide sequestration systems. Salt rock has favourable creep properties, enabling crack healing in relatively low-pressure and low-temperature conditions. Contrary to models proposed in continuum damage mechanics, creep models can predict damage increase and decrease. However, the formulation does not allow the modelling of time-independent crack opening and the resulting anisotropy of stiffness and deformation. Moreover, a distinction needs to be made between reversible and irreversible crack-induced deformation. A compression test including a healing phase has been simulated using a model in which healing of deformation and stiffness recovery are not clearly distinguished. The results show an inconsistency between deformation and healing evolutions. To overcome this problem, an alternative modelling framework is proposed to predict anisotropic healing deformation and stiffness recovery.
Stiffness and Deformation of Rock Subjected to Anisotropic Damage and Temperature-Dependent Healing

(Georgia Institute of Technology, 2012-06) Xu, Hao ; Arson, Chloé ; Chester, Fred M.

This research is motivated by the increasing need for geostorage facilities, mainly: nuclear waste disposals, high-pressure gas reservoirs and carbon dioxide sequestration systems. A new constitutive model is formulated to account for anisotropic damage due to tensile cracks and healing due to Diffusive Mass Transfer (DMT). The damage variable is the difference between the second-order crack density tensor and a scalar viscoplastic healing variable. The viscoplastic healing variable is needed to model the effects of DMT on the reduction of damage-induced deformation. Contrary to the damage and healing models proposed previously for salt rock, the proposed framework accounts for crack-induced anisotropy, and anisotropy is treated in both damage and healing evolution laws. Compression, extension and compression loading and unloading cycles have been simulated with Theta-Stock Finite Element code. The results illustrate well the influence of anisotropic damage on stiffness degradation and residual strain development. An algorithm has also been written to study the trends of the coupled damage and healing model for a stress path comprising an isotropic compression, and axial compression, a healing period and an unloading phase. The results match the theoretical expectations, and show that the proposed model can predict anisotropic damage and healing.