Modeling of Tensile and Compressive Damage in Layered Sedimentary Rock: A Direction Dependent Non-Local Model

(Georgia Institute of Technology, 2017-06) Wencheng, Jin ; Arson, Chloé

This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic transverse isotropy, e.g. sedimentary rocks with a bedding plane. The direction dependent mechanical response is captured by utilizing four types of equivalent strains, for tension and compression, parallel and perpendicular to the bedding plane. The model is calibrated against triaxial compression test data, for different confinement and loading orientations. The variations of uniaxial tensile and compressive strengths with the orientation of the loading relative to the bedding follow the trends and magnitudes noted in experiments. Anisotropic non-local equivalent strains were used in the formulation to avoid localization and mesh dependence encountered with strain softening. Two different internal length parameters are used to distinguish the non-local effects along and perpendicular to the bedding. An arc length control algorithm is used to avoid convergence issues. Results of three-point bending tests confirm that the nonlocal approach indeed eliminates mesh dependency. Results show that the orientation and size of the damage process zone are direction dependent, and that materials with intrinsic transverse isotropy exhibit mixed fracture propagation modes except when the bedding aligns with the loading direction. Further research towards a multiscale hydro-mechanical fracture propagation scheme is undergoing.
Non-Local Micromechanical Anisotropic Damage Modeling Of Quasi-Brittle Materials: Formulation And Implementation

(Georgia Institute of Technology, 2017-06) Wencheng, Jin ; Arson, Chloé

A nonlocal anisotropic damage model is proposed for quasi-brittle materials, such as concrete and rock. The local anisotropic damage model is formulated by combining a free energy derived from micromechanics with phenomenological yield criteria and damage potentials. The trace of the total strain is used to distinguish tensile and compressive loading paths, and to account for the influence of the confining pressure on the propagation of compression cracks. Yield criteria in tension and compression are expressed in terms of equivalent strains, which depend on the difference between principal strain components. A non-local measure of strain is used to avoid localization. Constitutive parameters are calibrated against published experimental data for concrete and shale. Simulations of three-point bending tests show that non-local enhancement is necessary and efficient to avoid mesh dependency upon strain softening. Simulations of borehole excavation damage zone show that the damage model is not mesh dependent upon stress hardening. Numerical predictions are in agreement with experimental observations and the model can capture unilateral effects, tensile softening, compressive hardening and confinement dependent compressive behavior.
A Method to Estimate the Energy Distribution During the Confined Comminution of Granular Materials

(Georgia Institute of Technology, 2017-06) Arson, Chloé ; Wang, Pei

During the confined comminution of granular materials, the work input is transformed into elastic energy stored in the grains, breakage energy used to generate new surfaces, energy dissipated by friction between grains in contact, and redistribution energy dissipated by the relative movement of crushed fragments. We assume that the expression of Particle Size Distribution (PSD) in a crushed sample is a function of a fractal distribution and a uniform distribution. This allows calculating the breakage parameter, the increase of surface energy, and finally the energy dissipated by breakage. By summing the contact energy at all the contacts within a sample, we calculate the elastic energy stored. The calculation of friction-dissipated energy requires calculating relative movements of contacts, which are highly unpredictable especially when crushing is involved. Thus we include the dissipation that results from the relative displacement of grains in contact (including both crushed fragments and surrounding intact grains) in the friction-dissipated energy. We obtain the friction-dissipated energy by subtracting the elastic energy stored in the grains and the breakage energy from the input energy. The results show that the energy distribution is stress sensitive and changes a lot with the increase of compressive stress. Energy dissipation by friction plays a major role during confined comminution.
Numerical Study of Thermo-Mechanical Effects on the Viscous Damage Behavior of Rock Salt Caverns

(Georgia Institute of Technology, 2017-06) Cheng, Zhu ; Shen, Xianda ; Arson, Chloé ; Pouya, Ahmad

Underground cavities in rock salt have received increased attention for the storage of oil, gas, and compressed air energy. In this study, the transition between secondary and tertiary creep in salt is determined by a micro-macro model: The initiation of grain breakage is correlated with the acceleration of viscoplastic deformation rate and with the initiation of damage at the macroscopic scale. Salt stiffness decreases when macroscopic damage increases, which allows predicting the evolution of the damage zone around salt caverns used for geological storage. After implementing the phenomenological model into the Finite Element Method (FEM) program POROFIS, two thermo-mechanical coupled stress paths are simulated to analyze stress concentrations and viscous damage around a 650-m-deep cavern in axisymmetric conditions. Numerical results indicate that, despite the pressurization or depressurization-induced temperature variation, internal gas temperature always tends to approach the primary surrounding rock mass value. The viscous deformation induced by thermo-mechanical couplings significantly affects the original stress field at the cavern wall and induces high damage at the most concave sections of the cavern. Results reveal the significant influences of idle time, gas pressure range, and injection and withdrawal cycles on stress, strain and temperature distributions in the vicinity of the cavern. More analyses are needed to confirm the influence of thermo-mechanical cycles of pressurization and depressurization, and to design long-term cavern operations.
Bio-Inspired Fluid Extraction Model for Reservoir Rocks

(Georgia Institute of Technology, 2017-06) Patino-Ramirez, Fernando ; Arson, Chloé

Biological and engineering flow systems maximize their efficiency by following the path of minimum energy over the domain they are embedded in. This fact motivates the present research, since industrial fluid extraction and injection processes are designed to minimize the implementation cost (energy, materials) and maximize the volume of fluid injected (or withdrawn). This work presents a bio-inspired fluid flow model to optimize the path that connects resource-rich pores in a rock. We explain the commonalities between the equations governing flow in a porous medium and growth of slime mold, an organism that dynamically deploys tube-like structures and adapts them as a function of their contribution to the overall network. We perform several simulations to analyze the influence of the pore size distribution and of pore spatial distribution on the topology of the extraction network predicted by the slime mold growth algorithm. We discuss the suitability of the biomimicry model to design fracture patterns for optimal fluid extraction from a porous rock.
Microcrack Network Development in Salt-Rock During Cyclic Loading at Low Confining Pressure

(Georgia Institute of Technology, 2017-06) Ding, Jihui ; Chester, Frederick M. ; Chester, Judith S. ; Xianda, Shen ; Arson, Chloé

Triaxial compression tests of synthetic salt-rock are conducted to investigate microfracture development in a semibrittle polycrystalline aggregate. The salt-rock is produced from uniaxial consolidation of granular halite at 150 °C. Following consolidation, the sample is deformed by cyclic loading at room temperature and low confining pressure (Pc = 1 MPa). Load cycles are performed within the elastic regime, up to yielding, and after successive increments of steady ductile flow. At the tested conditions, the samples exhibit ductile behavior with slight work hardening. The microstructure at different stages of deformation indicates that grain-boundary cracking is the dominant brittle deformation mechanism. Microcracking is influenced by the loading configuration and the geometric relationships between neighboring grains. These microcracks display a preferred orientation parallel to the load axis. With cyclic loading, microcracks increase in density and form linked arrays parallel to the direction of loading. As the linked arrays lengthen, grain contacts are progressively opened, which eventually leads to loss of cohesion along surfaces parallel to the loading direction. The observations of crack-network development in salt-rock can improve our understanding of progressive damage and spalling at salt cavern walls.
Experimental Characterization of Microstructure Development for Calculating Fabric and Stiffness Tensors in Salt Rock

(Georgia Institute of Technology, 2017-06) Xianda, Shen ; Arson, Chloé ; Ding, Jihui ; Chester, Frederick M. ; Chester, Judith S.

Uniaxial consolidation tests were conducted on reagent-grade granular salt in dry conditions at 150 C. 2Dmicroscopic images, parallel to the axis of consolidation, were obtained at several stages of progressive consolidation from 15% to 3% porosity. Microstructure image analyses were performed to obtain probability density functions (PDFs) of the area, solidity, coordination number, orientation, elongation and roundness of the grains, as well as the PDFs of the branch lengths, branch orientations and solid volume fraction, defined locally over polygons with edges matching grain centroids. It is found that sample deformation is mostly due to grain rearrangement and that upon consolidation, grains become less convex, and elongate in the direction perpendicular to the loading axis. Four fabric tensors were calculated to assess microstructure anisotropy induced by grain orientation, branch length orientation, grain solidity and local solid volume fraction. Fabric tensors were diagonal and orthogonal. Therefore, their product was used to define a global fabric tensor, which was introduced in the expression of the stiffness tensors. The constitutive parameters were calibrated against the consolidation tests. The approach paves the way to enrich continuum damage and healing mechanics model with fabric descriptors that can play the role of internal variables.
Damage and healing model of stiffness and permeability for salt rock: microstructure imaging, fabric processes and continuum mechanics

(Georgia Institute of Technology, 2016-06) Zhu, Cheng ; Arson, Chloé

In this study, we proposed a fabric-enriched Continuum Damage Mechanics model to investigate the coupled influence of damage and healing on the mechanical and transport properties of salt rock. In order to infer the form of fabric tensors, we carried out creep tests on granular salt assemblies under constant temperature and humidity conditions and used micro-computed tomography for microstructure characterization. Using microscope imaging and micro-CT scanning, we analyzed the probability distributions of crack radius, void areas and crack spacing and used them as a basis to derive macroscopic evolution laws. A stress path comprising a tensile loading, a compressive unloading, a creep-healing stage, and a reloading was simulated. As expected, stiffness decreases (respectively increases) and permeability increases (respectively decreases) upon damage (respectively healing). Results also highlight the increased efficiency of healing with temperature. The micro-macro relationships established by statistical image analysis also provide the evolution of microstructure descriptors during the test. Simulations show that permeability changes are controlled by changes in crack connectivity, which dominate changes of porosity. The proposed framework is expected to improve the fundamental understanding of coupled processes that govern microstructure changes and subsequent variations of stiffness and permeability in salt rock, which will allow the assessment of the long-term performance of geological storage facilities.
Simulation of mode II unconstrained fracture path formation coupled with continuum anisotropic damage propagation in shale

(Georgia Institute of Technology, 2016-06) Jin, Wencheng ; Arson, Chloé

The objective of this work is to simulate mode II multi-scale fracture propagation in shale by coupling a continuum anisotropic damage model with a Cohesive Zone Model (CZM). The Continuum Damage Mechanics – based Differential Stress Induced Damage (DSID) model is used to represent micro-scale crack evolution. DSID parameters were calibrated against pre-peak points of stress/strain curves obtained experimentally during triaxial compression tests performed in Bakken shale. A bilinear CZM is employed to represent macroscale fracture propagation. We calculated the effective shear modulus of a continuum that contained a distribution of parallel cracks according to the DSID model (which does not account for crack interactions) and according to Kachanov’s micromechanical model (which accounts for crack interactions). Simulations confirmed that above a crack density or damage of 0.3, crack interactions could not be ignored, and we used that threshold to define the transition between continuum damage propagation and discrete fracture propagation and subsequently, to calibrate the shear cohesive strength of the CZM. The CZM cohesive energy release rate was determined by calibrating a numerical model of triaxial compression test against experimental data obtained on Bakken shale. The cylindrical sample was modeled with a CZM to pre-define an inclined cohesive fracture, and the DSID model was assigned to the surrounding elements. We used our calibrated CZM-DSID model to simulate a biaxial compression test in plane strain. Results clearly show that the proposed modeling strategy not only allows simulating the advancement of macro-fracture tips, but also captures the inception and growth of micro-cracks that form damaged zones, as well as the transition between smeared damage and discrete fracture.
Mechanical Behavior and Microstructure Development in Consolidation of Nominally Dry Granular Salt

(Georgia Institute of Technology, 2016-06) Ding, Jihui ; Chester, Frederick M. ; Chester, Judith S. ; Zhu, Cheng ; Arson, Chloé

Uniaxial consolidation of granular salt is carried out to study the mechanical behavior and fabric development in a material that deforms by microscopic brittle and intracrystalline-plastic processes. Dry granular salt is sieved to produce well-sorted size fractions. The granular salt is consolidated in a heated cell at axial stresses up to 90 MPa and temperatures of 100 - 200 ˚C to document stress-consolidation relationships and microstructural development. Polished and chemically-etched petrographic sections of salt samples prior to and after deformation at 150˚C are studied using transmitted- and reflected-light optical microscopy. We show that temperature has profound effect on porosity reduction during consolidation. At tested conditions, the dominant deformation mechanism is crystal plasticity; brittle deformation is largely suppressed. Samples consolidated at higher maximum axial stress develop higher overall dislocation densities. The distribution of dislocations, however, is strongly heterogeneous from grain to grain because of the complex grain-scale loading geometries and the distribution of intragranular flaws such as fluid inclusions. Static recrystallization occurs in some highly strained areas, but overall is minor at 150˚C. The experiments help to improve our understanding of consolidation, and serve to guide the fabrication of synthetic rock salt as experimental material, as well as to inform and test constitutive models of deformation of granular salt for engineering needs.