Damage and healing mechanics of salt rocks

Anisotropy of rock stiffness and deformation induced by crack debonding, opening, closure and rebonding

A thermodynamic framework based on Continuum Damage Mechanics is proposed to model the effects of Thermo-Mechanical coupled stresses on stiffness anisotropy induced by crack opening and closure in rock. 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. 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. The model will be improved to account for hysteretic effects observed during cyclic thermo-mechanical stress paths, and to distinguish closure and healing regimes.

Pictures: Zhu et al., 2013; Zhu and Arson, 2013

Microstructure-enriched model of damage and healing for salt rock

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 occur wihin 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 (CDM) 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.

Pictures: Zhu and Arson, 2014

Moments of probability of fabric descriptors are used to find relationships between microstructural and phenomenological variables. Creep processes in salt include glide, cross-slip, diffusion, and dynamic recrystallization. We assume that healing is predominantly governed by diffusive mass transfer. We model the corresponding crack cusp propagation on grain faces by means of a two-dimensional diffusion equation. We calibrate this grain-scale healing model against experimental measures of crack cusp propagation distance. We simulate the opening, closure and rebonding of three orthogonal families of micro-cracks during a compression-tension loading cycle. Multi-scale model predictions illustrate the evolution of stiffness, deformation, and crack geometry during the anisotropic damage and healing process, and highlight the increased healing efficiency with time. The proposed modeling approach is expected to provide more precise and reliable performance assessments on geological storage facilities in salt rock.

Pictures: Zhu and Arson, 2015

Current modeling effort focus on salt 3D imaging and enhanced image analysis for the prediction of crack coalescence and percolation thresholds.

Pictures: Zhu, 2015

Experimental study of the role of salt specific surface in healing processes driven by diffusion and pressure solution

In this research, uniaxial compaction experiments were conducted under a chemically closed system (i.e. no long mass transfer) on brine saturated and n-decane filled granular salt to investigate the role of salt specific surface area in controlling healing processes and creep by diffusive mass transport and pressure solution. The effect on grain size (50-90 microns; 90-125 microns; 125-150 microns), applied stress (0.175; 0.811; 1.88; 2.75 MPa) and pore fluid are investigated to get insight into the mechanisms operating. Long-term compaction experiments are conducted and show a change in mechanism during the healing process and densification at lower porosities as predicted by theoretical models. The mechanical results obtained by short term compaction experiments show that for the brine filled samples an increase in compaction rate is promoted by an increase in applied stress and a decrease in grain size. Addition of n-decane counteracting on dissolution and precipitation processes and blocks the compaction process completely, independent of grain size. Microstructural observations for the brine saturated samples show pressure solution like structures as truncations (t), grain to grain indentations (i), overgrowths (o) at lower volumetric strains, but also necking (n) and grain growth at higher volumetric strains. The existing models assume a geometry of a simple cubic pack of spherical grains and seems applicable for diffusion controlled pressure solution creep in granular salt for low strain regimes (up to 10%). Microstructural analysis shows an increase in contact area and decrease in pore wall area with decreasing porosity.

Pictures: Douma, 2015

Micro-macro modeling of salt rock viscous fatigue under cyclic loading

Underground cavities in salt rock formations used for Compressed Air Energy Storage (CAES) undergo cyclic loads and are subject to a fatigue phenomenon that induces a decrease of rock strength and stiffness. A micromechanical analysis of this phenomenon is necessary to understand its mechanisms and elaborate relevant constitutive models. The polycrystalline nature of rock salt has a crucial effect on crack propagation and rock damage and, hence, on fatigue behavior. This behavior was investigated on the basis of self consistent upscaling approaches for viscous heterogeneous materials. The internal stresses in the polycrystal were modeled based on experimental data available for halite single crystals. The simulation of monotonic compression tests allowed tracking the triggering of fatigue damage. Results showed that tensile stresses are developed in the polycrystal under global compressive load, the amplitude of which depends on the macroscopic load rate or frequency. The figures below show that higher microstresses develop when the spemcimen is subjected to a higher number of loading cycles. The goal of this research project is to model the macroscopic damage induced by the breakage of grains that undergo microscopic stresses that exceed halite tensile strength.

Pictures: Zhu, Pouya and Arson, 2015

Comparison between inclusion-matrix and Finite Element models of salt rock viscous fatigue

Laboratory tests were simulated with POROFIS, by using two different models: (1) A continuous domain in which Finite Elements (FE) are assigned the micro-macro inclusion-matrix homogenization model presented above; (2) A mesh with FE for the solid grains and joint elements for the porous space. The performance of the inclusion-matrix model is assessed based on the difference between predictions given by the two models, which indicates whether the homogenization scheme can avoid meshing the crystallographic structure of rocks and save computational time. Preliminary results shown in the figures below indicate that the transition between secondary and tertiary creep in salt rock is caused by crack coalescence.

Pictures: Zhu, Pouya and Arson, 2015