Micro-macro Damage and Healing Mechanics of Crystalline and Porous Media
Georgia Institute of Technology
Problems
In crystalline and porous media, damage and healing refer to variations of mechanical and physical properties induced by pore or crack evolution. The gap between microscopic and macroscopic models makes it infeasible to uniquely characterize the pore- and crack- scale mechanisms that control deformation and flow regimes, predict percolation thresholds coupled to changes of rock stiffness, or relate crack rebonding time to stiffness and permeability healing time. The goal of our research is, therefore, to understand and predict chemo-mechanical damage and healing processes by coupling microstructural and poromechanical models. Fundamental scientific questions include: Why do pores and cracks heal? How long do mechanical and hydraulic recovery take? How much energy does healing require?
Approach
To establish closed forms that relate microstructure changes to macroscopic damage and healing evolution, we use both bottom-up and top-to-bottom approaches. In the former, moments of probability density functions of microstructure descriptors define fabric tensors that are used as dissipation variables at the macroscale. In the latter, homogenization schemes are built for polycrystals and for porous media with inclusions endowed with eigenstress. Fabric-enriched and matrix-inclusion models are inspired from and validated against laboratory experiments and image analyses. After calibration and validation at the material point, models are implemented in codes based on the Finite Element Method (FEM) and the eXtended Finite Element Method (XFEM). When the continuum assumption cannot hold, at a given damage threshold, a cohesive segment is inserted in replacement of a portion of the damage process zone. Rigorous calibrations procedures for the cohesive strength and the cohesive energy release rate ensure the balance of energy dissipated at the micro and macro scales. In order to simulate multi-scale fracture propagation driven by fluid injection, interpolation on fracture elements is enriched with jump functions for displacements, and with level-set-based distance functions for fluid pressure, which ensures that displacements are discontinuous across the fracture, but that the pressure field remains continuous.
Findings
A micromechanical model allowed predicting damage induced by a set of crack families subject to mixed mode propagation. A phenomenological approach was also proposed to relate micro-crack density, deformation and stiffness variations by deriving damage and healing dissipation potentials. Thermodynamic consistency is ensured, even when multiple damage and healing mechanisms are coupled. Upscaling was done by enriching the macroscopic formulation with fabric tensors defined as moments of probability of crack length, crack spacing, local porosity, pore. Additionally, self-consistent homogenization schemes were established to model viscous damage and pressure-solution driven healing in salt rock and implemented in the FEM to simulate long-term storage in caverns. We used a Mori-Tanaka homogenization scheme to capture the stress redistribution and subsequent damage induced by the expansion of biotite minerals as they convert to vermiculite over time. Biotite chemical weathering was accounted for by introducing inclusions' eigenstrains in the formulation. Simulations show that, at typical saprolite depth, micro-crack propagation can be controlled by weathering. Under constrained displacements, mechanical damage triggers earlier if the biotite volume fraction is high or if biotite minerals present a large orientation angle compared to the horizontal. A computational tool was developed to simulate the propagation of a discrete fracture within a continuum damage process zone. An XFEM was proposed to simulate multi-scale fracture propagation driven by fluid injection in transverse isotropic porous media. Intrinsic anisotropy was accounted for at the continuum scale, by using a non-local damage model in which four equivalent strains are defined to distinguish tension and compression, parallel and perpendicular to the bedding. Simulation results highlight the influence of intrinsic anisotropy on fluid driven fracture propagation.
Impact
Energy demand, environment protection and public health preservation raise pressing needs for safe and sustainable geological storage systems. The mining operations required to recover mineral resources, store energy underground and dispose of waste in deep geological layers involve coupled mechanical, physical and chemical rock microstructure changes. Our research findings can be used to recommend the conditions of moisture and temperature necessary to minimize damage and/or enhance healing in rocks and to design safe and sustainable geological storage systems. In addition to preventing subsidence, borehole instabilities and contaminant leakage, the proposed models will be applicable for predicting fault rupture during earthquakes, improving manufacturing methods and designing sustainable materials. Original contributions include: A theory to predict pore geometry evolution upon multi-physics damage and healing processes; Creative mathematical models to describe pore network topology with geometric variables that control damage and healing; Fundamental relationships between pore-scale healing time and macroscopic mechanical recovery time - a step forward to bridge poromechanics and damage mechanics; Innovative computational methods to predict mechanical instabilities and percolation thresholds upon damage and healing; Realistic multi-physics simulations of geological storage. The rigorous integration of topology, thermodynamics, poromechanics and continuum mechanics will transform the theory of damage and healing mechanics and provide a framework to interpret rock stress path history from topology descriptors.
Core competencies
- Damage and fracture mechanics
- Micromechanics
- Poromechanics
- Homogenization theory
- Computational Geomechanics
- Image processing and analysis
- Bio-inspired calibration algorithms and network dynamics programs
Current research team members
- Xianda Shen
- Fernando Patino-Ramirez
- Koochul Ji
- Tingting Xu
- Haozhou He
- Floriana Anselmucci
Recent graduates
- Dr. Pei Wang, Georgia Institute of Technology
- Dr. Wencheng Jin, Idaho National Laboratory
- Dr. Cheng Zhu, Rowan University
- Dr. Hao Xu, Lawrence Berkeley National Laboratory
Collaborators
- Dr. Antonia Antoniou, Georgia Institute of Technology
- Dr. Sébastien Brisard, Ecole des Ponts Paris Tech, France
- Dr. Bernardo Caicedo, University of the Andes, Colombia
- Dr. Sheng Dai, Georgia Institute of Technology
- Dr. Audrey Dussutour, Toulouse University