Micro-Macro Damage and Healing Rock Mechanics

Abstract:

Why do some granite bedrocks exhibit metric-scale spheroidal fractures? Why does salt creep accelerate? Can underground salt storage facilities heal over time? Rocks have astonishing and intriguing properties. In this talk, we focus on mechanical damage and healing. We use the theory of homogenization to explain the pore- and crack- scale mechanisms that control rock deformation, stiffness variations and strength changes. Rock is studied at the scale of a Representative Elementary Volume (REV), which is typically two to three orders of magnitude larger than the cracks or minerals that are assumed to influence damage and healing. The REV is modeled as a homogenous matrix that contains inclusions, for instance cracks or crystals. Inclusions are gathered in families, depending on their geometry, constitutive law or prestress. The stress-strain relationship at the REV scale is found by solving an inclusion-matrix problem. In this talk, we solve the inclusion-matrix problem by using either the Mori-Tanaka (MT) or the Self-Consisent (SC) scheme. The MT scheme is appropriate for rocks that contain cracks or inclusions that interact with each other via the matrix, while the SC scheme is suitable when there is no matrix and inclusion volume fractions are similar. In granite, the expansion of biotite minerals upon weathering is thought to be the cause of spheroidal fractures. A time-dependent deformation law is established at the biotite crystal scale, which yields the eigenstrain of each biotite inclusion. A MT homogenization scheme is used to simulate biotite weathering under various boundary conditions. Results show that bedrock damage during biotite oxidation is not significantly influenced by the orientation of regional stresses and could alter tectonic fracture patterns. We then use the SC approach to model salt, a monomineralic rock often considered for geological storage, due to its favorable creep and self-healing properties. First, we homogenize the behavior of visco-plastic mono-crystal inclusions that can break under tensile stress.  Simulations provide micro-mechanical interpretations to strain hardening, creep recovery, damage and accelerated creep, as well as shakedown during cyclic loading. FEM simulations of salt cavern depressurization clearly highlight the formation of a damaged zone over time. Second, we consider a different type of inclusion to model healing by pressure solution, a process by which salt dissolves at grain contacts and precipitates in the pores. Sensitivity analyses show that when initial voids have different sizes, larger pores have a negligible precipitation rate and slow down the overall REV healing process. FE simulations of healing after cavern sealing suggest that pressure solution increases convergence and that healing is self-limited. This result calls for a more sophisticated model coupling the counter-acting effects of dislocation glide and pressure solution. We thus conclude the talk by presenting the outline of a unified self-consistent approach to model multiple time-dependent microscopic mechanisms that jointly result in damage or healing at the macroscopic scale.

Bio:
Dr. Chloé Arson is an Associate Professor in the School of Civil and Environmental Engineering (CEE) at the Georgia Institute of Technology (Georgia Tech). She earned a M.Sc. in soil and rock mechanics (2006) and a Ph.D. in geomechanics
(2009) at Ecole des Ponts Paris Tech (France). Dr. Arson’s research is in damage and healing mechanics, homogenization theory, computational geomechanics, numerical modeling of multi-scale fracture propagation, underground storage and bio-inspired burrowing mechanics. Dr. Arson chairs the EMI Poromechanics Committee and she serves as the Associate Editor of the Journal of Rock Mechanics and Rock Engineering and of the Journal of Engineering Mechanics. Dr. Arson received two PhD research prizes in 2010, the NSF CAREER award in 2016 and the  inter-disciplinary research award of Georgia Tech School of CEE in 2017.