Hamed Amiri

and 4 more

Key to most subsurface processes is to determine how structural and topological features at small length scales, i.e., the microstructure, control the effective and macroscopic properties of earth materials. Recent progress in imaging technology has enabled us to visualise and characterise microstructures at different length scales and dimensions. An approach to characterisation is the sampling of n-point correlation functions - known as statistical microstructural descriptors (SMDs) - from images. SMDs can then be used to generate statistically equivalent structures having larger sizes and additional dimensions – this process is known as $reconstruction$. We show that a deep-convolutional generative adversarial network trained with Wasserstein-loss and gradient penalty (WGAN-GP) results in a stable training and high-quality reconstructions of two-dimensional electron microscopy images of complex rock samples. To evaluate reconstruction performance, n-point polytope functions are calculated in both reconstructed and original microstructures and mean square error between them is used as a quality metric. These n-point polytope functions provide statistical information about symmetric, user-oriented higher-order geometrical patterns in microstructures. Our results show that GANs can naturally capture these higher-order statistics at short and long ranges. Furthermore, we compare our model with a benchmark stochastic reconstruction method based solely on two-point correlation. Our findings indicate that although yielding the same two-point statistics, two microstructures can be morphologically and structurally different, emphasising the need for coupling higher-order correlation functions with reconstruction methods. This is a critical step for future schemes that aim to reconstruct complex heterogeneous systems and couple microstructures to macroscopic phenomena.

Markus Ohl

and 5 more

The spatial separation of macroscopic rheological behaviours has led to independent conceptual treatments of frictional failure, often referred to as brittle, and viscous deformation. Detailed microstructural investigations of naturally deformed carbonate rocks indicate that both, frictional failure, and viscous mechanisms might operate during seismic deformation of carbonates. Here, we investigate the deformation mechanisms that were active in two carbonate fault zones in Greece by performing detailed slip-system analyses on data from automated crystal-orientation mapping transmission electron microscopy and electron backscatter diffraction. We combine the slip system analyses with interpretations of nanostructures and predictions from deformation mechanism maps for calcite. The nanometric grains at the principal slip surface should deform by diffusion creep but the activation of the (0001)<-12-10> slip system is evidence for a contribution of crystal plasticity. A similar crystallographic preferred orientation appears in the cataclastic parts of the fault rocks despite exhibiting a larger grain size and a different fractal dimension, compared to the principal slip surface. The cataclastic region exhibits microstructures consistent with activation of the (0001)<-12-10> and {10-14}<-2021> slip systems. Post-deformational, static recrystallisation and annealing produces an equilibrium microstructure with triple junctions and equant grain size. We propose that repeated introduction of plastic strain and recrystallisation reduces the grain size and offers a mechanism to form a cohesive nanogranular material. This formation mechanism leads to a grain-boundary strengthening effect resulting in slip delocalisation which is observed over six orders of magnitude (μm–m) and is expressed by multiple faults planes, suggesting cyclic repetition of deformation and annealing.
Deformation at tectonic plate boundaries involves coupling between rock deformation, fluid flow and metamorphic reactions, but quantifying this coupling is still elusive. We present a new two-dimensional hydro-mechanical-chemical numerical model and investigate the coupling between heterogeneous rock deformation and metamorphic (de)hydration reactions. Rock deformation consists of linear viscous compressible and power-law viscous shear deformation. Fluid flow follows Darcys law with a Kozeny-Carman type permeability. We consider a closed isothermal system and the reversible (de)hydration reaction: periclase and water yields brucite. In the models, fluid pressure within a circular or elliptical inclusion is initially below the periclase-brucite reaction pressure, and above in the surrounding. Inclusions exhibit a shear viscosity thousand times smaller than for the surrounding, because we assume that periclase-water and brucite regions have different effective viscosities. In models with circular inclusions, solid deformation has a minor impact on the evolution of fluid pressure, porosity and reaction front. Models with elliptical inclusions and far-field shortening generate higher rock pressure inside the inclusion compared to circular inclusions, and show a faster reaction-front propagation. The propagating reaction-front increases the inclusion surface and causes an effective, reaction-induced weakening of the heterogeneous rock. Weakening evolves strongly nonlinear with progressive strain. Distributions of fluid and rock pressure as well as magnitudes and directions of fluid and solid velocities are significantly different. The models mimic basic features of shear zones and plate boundaries and suggest a strong impact of heterogeneous rock deformation on (de)hydration reactions and associated reaction-induced weakening. The applied MATLAB algorithm is provided.