Cheng Zhu

A Model of Damage and Healing Coupling Halite Thermo-mechanical Behavior to Microstructure Evolution

Abstract Creep processes in halite (salt rock) include glide, cross-slip, diffusion and dynamic recrystallization. Diffusive mass transfer (DMT) can result in crack rebonding, and mechanical stiffness recovery. Crack rebonding driven by DMT occurs within a few days at room temperature and low pressure. DMT is enhanced at higher temperatures, which could be beneficial for the sustainabilty of geological storage facilities in salt mines. On the one hand, visco-plastic laws relating creep microscopic processes to microstructure changes are empirical. On the other hand, theoretical models of damage and healing disconnect thermodynamic variables from their physical meaning. The proposed model enriches the framework of continuum damage mechanics with fabric descriptors. In order to infer the form of fabric tensors from microstructure observation, creep tests were carried out on granular salt under constant stress and humidity conditions. The evolution of net damage is governed by a diffusion equation, in which the characteristic time scales with the typical size of halite crystals, and the diffusion coefficient is a function of temperature. A stress path comprising a tensile loading, a compressive unloading, a creep–healing stage and a reloading was simulated. Macroscopic and microscopic model predictions highlight the increased efficiency of healing with time and temperature. The model presented in this paper is expected to improve the fundamental understanding of damage and healing in rocks at both macroscopic and microscopic levels, and the long-term assessment of geological storage facilities.

Micro-Macro Analysis and Phenomenological Modelling of Salt Viscous Damage and Application to Salt Caverns

AbstractThis paper aims to gain fundamental understanding of the microscopic mechanisms that control the transition between secondary and tertiary creep around salt caverns in typical geological storage conditions. We use a self-consistent inclusion-matrix model to homogenize the viscoplastic deformation of halite polycrystals and predict the number of broken grains in a Representative Elementary Volume of salt. We use this micro-macro modeling framework to simulate creep tests under various axial stresses, which gives us the critical viscoplastic strain at which grain breakage (i.e., tertiary creep) is expected to occur. The comparison of simulation results for short-term and long-term creep indicates that the initiation of tertiary creep depends on the stress and the viscoplastic strain. We use the critical viscoplastic deformation as a yield criterion to control the transition between secondary and tertiary creep in a phenomenological viscoplastic model, which we implement into the Finite Element Method program POROFIS. We model a 850-m-deep salt cavern of irregular shape, in axis-symmetric conditions. Simulations of cavern depressurization indicate that a strain-dependent damage evolution law is more suitable than a stress-dependent damage evolution law, because it avoids high damage concentrations and allows capturing the formation of a damaged zone around the cavity. The modeling framework explained in this paper is expected to provide new insights to link grain breakage to phenomenological damage variables used in Continuum Damage Mechanics.

Modeling the Influence of Thermo-Mechanical Crack Opening and Closure on Rock Stiffness

A thermodynamic framework is proposed to model the effect of mechanical stress and temperature on crack opening and closure 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 induced by damage. Crack closure is modeled through unilateral effects produced on rock stiffness. Simulations show that: (1) under anisotropic mechanical boundary conditions, crack closure occurs during cooling, (2) the thermo-mechanical strain energy necessary to close cracks during cooling is larger than the strain energy needed to close the cracks by mechanical compression. Parametric study highlights the thermo-mechanical stress redistributions occurring during closure. The proposed framework is expected to bring new insights in the design and reliability assessment of geotechnical reservoirs and repositories.

Self-consistent micromechanical approach for damage accommodation in rock-like polycrystalline materials

In quasi-brittle polycrystalline materials, damage by cracking or cleavage dominates plastic and viscous deformation. This paper proposes a micromechanical model for rock-like materials, incorporating the elastic-damage accommodation of the material matrix, and presents an original method to solve the system of implicit equations involved in the formulation. A self-consistent micromechanical approach is used to predict the anisotropic behavior of a polycrystal in which grain inclusions undergo intragranular damage. Crack propagation along planes of weakness with various orientation distributions at the mineral scale is modeled by a softening damage law and results in mechanical anisotropy at the macroscopic scale. One original aspect of the formulated inclusion–matrix model is the use of an explicit expression of Hill’s tensor to account for matrix ellipsoidal anisotropy. To illustrate the model capabilities, a uniaxial compression test was simulated for a variety of polycrystals made of two types of mineral inclusions with each containing only one plane of weakness. Damage always occurred in only one mineral type: the damaging mineral was that with a smaller shear modulus (respectively higher bulk modulus) when bulk modulus (respectively shear modulus) was the same. For two minerals with the same shear moduli but different bulk moduli, the maximum damage in the polycrystal under a given load was obtained at equal mineral fractions. However, for two minerals with different shear moduli, the macroscopic damage was not always maximum when the volume fraction of two minerals was the same. When the weakness planes’ orientations in the damaging mineral laid within a narrow interval close to the loading direction, the macroscopic damage behavior was more brittle than when the orientations were distributed over a wider interval. Parametric studies show that upon proper calibration, the proposed model can be extended to understand and predict the micro–macro behavior of different types of quasi-brittle materials.

Theoretical Bases of A Thermo-Mechanical Damage and DMT-Healing Model for Rock

A theoretical framework is proposed to model thermo-mechanical (TM) crack opening, closure, and healing in rock. The model is based on Continuum Damage Mechanics and thermodynamics. The postulated free energy is a polynomial of deformation, temperature, damage and healing. The damage-driving force captures damage evolution due to mechanical or TM tensile stresses, as well as the decrease of material toughness at elevated temperature. Crack closure is modeled by adopting the concept of unilateral effect on rock stiffness. A mixed variable is introduced to account for anisotropic TM damage and rate-dependent healing. Crack rebonding is assumed to result from Diffusive Mass Transfer (DMT) processes, and accordingly, the healing evolution law is governed by the diffusion equation. Contrary to other models for rock, the healing deformation is not a creep volumetric deformation, but the difference between the deformation before and after DMT. A parametric study illustrates the model capabilities: the simulation of TM stress paths with higher degree of mechanical recovery for longer healing time or higher healing temperature. The proposed model is expected to better predict the long-term behavior of selfhealing rock materials – containing clay of halite minerals for instance.