Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations

Tomographic images taken inside and outside a compaction band in a field specimen of Aztec sandstone are analyzed by using numerical methods such as graph theory, level sets, and hybrid lattice Boltzmann/finite element techniques. The results reveal approximately an order of magnitude permeability reduction within the compaction band. This is less than the several orders of magnitude reduction measured from hydraulic experiments on compaction bands formed in laboratory experiments and about one order of magnitude less than inferences from two-dimensional images of Aztec sandstone. Geometrical analysis concludes that the elimination of connected pore space and increased tortuosities due to the porosity decrease are the major factors contributing to the permeability reduction. In addition, the multiscale flow simulations also indicate that permeability is fairly isotropic inside and outside the compaction band

Effective Normal Stress Alteration due to Pore Pressure Changes Induced by Dynamic Slip Propagation on a Plane Between Dissimilar Materials

Recent, detailed examinations of fault zones show that walls of faults are often bordered by materials that are different from each other and from the more uniform material farther away. In addition, they show that the ultracataclastic core of mature fault zones, where slip is concentrated, is less permeable to flow across it than the adjoining material of the damage zone. Inhomogeneous slip at the interface between materials with different poroelastic properties and permeabilities causes a change in pore pressure there. Because slip causes compression on one side of the fault wall and extension on the other, the pore pressure on the fault increases substantially when the compressed side is significantly more permeable and decreases when, instead, the extended side is more permeable. This change in pore pressure alters the effective normal stress on the slip plane in a way that is analogous to the normal stress alteration in sliding between elastically dissimilar solids. The magnitude of the effect due to induced pore pressure can be comparable to or larger than that induced by sliding between elastic solids with a dissimilarity of properties consistent with seismic observations. The induced pore pressure effect is increased by increasing contrast in permeability, but the normal stress alteration due to elastic contrast increases rapidly as the rupture velocity approaches the generalized Rayleigh velocity. Because the alteration in effective normal stress due to either effect can be positive or negative, depending on the contrast in properties, the two effects can augment or offset each other.Earth and Planetary SciencesEngineering and Applied Science

Stability and Localization of Rapid Shear in Fluid-Saturated Fault Gouge: 2. Localized Zone Width and Strength Evolution

Field and laboratory observations indicate that at seismic slip rates most shearing is confined to a very narrow zone, just a few tens to hundreds of microns wide, and sometimes as small as a few microns. Rice et al. (2014) analyzed the stability of uniform shear in a fluid-saturated gouge material. They considered two distinct mechanisms to limit localization to a finite thickness zone, rate-strengthening friction, and dilatancy. In this paper we use numerical simulations to extend beyond the linearized perturbation context in Rice et al. (2014), and study the behavior after the loss of stability. Neglecting dilatancy we find that straining localizes to a width that is almost independent of the gouge layer width, suggesting that the localized zone width is set by the physical properties of the gouge material. Choosing parameters thought to be representative of a crustal depth of 7 km, this predicts that deformation should be confined to a zone between 4 and 44 μm wide. Next, considering dilatancy alone we again find a localized zone thickness that is independent of gouge layer thickness. For dilatancy alone we predict localized zone thicknesses between 1 and 2 μm wide for a depth of 7 km. Finally, we study the impact of localization on the shear strength and temperature evolution of the gouge material. Strain rate localization focuses frictional heating into a narrower zone, leading to a much faster temperature rise than that predicted when localization is not accounted for. Since the dynamic weakening mechanism considered here is thermally driven, this leads to accelerated dynamic weakening.Earth and Planetary SciencesEngineering and Applied Science

Stability and Localization of Rapid Shear in Fluid-Saturated Fault Gouge: 1. Linearized Stability Analysis

Field observations of major earthquake fault zones show that shear deformation is often confined to principal slipping zones that may be of order 1–100 μm wide, located within a broader gouge layer of order 10–100 mm wide. This paper examines the possibility that the extreme strain localization observed may be due to the coupling of shear heating, thermal pressurization, and diffusion. In the absence of a stabilizing mechanism shear deformation in a continuum analysis will collapse to an infinitesimally thin zone. Two possible stabilizing mechanisms, studied in this paper, are rate-strengthening friction and dilatancy. For rate-strengthening friction alone, a linear stability analysis shows that uniform shear of a gouge layer is unstable for perturbations exceeding a critical wavelength. Using this critical wavelength we predict a width for the localized zone as a function of the gouge properties. Taking representative parameters for fault gouge at typical centroidal depths of crustal seismogenic zones, we predict localized zones of order 5–40 μm wide, roughly consistent with field and experimental observations. For dilatancy alone, linearized strain rate perturbations with a sufficiently large wavelength will undergo transient exponential growth before decaying back to uniform shear. The total perturbation strain accumulated during this transient strain rate localization is shown to be largely controlled by a single dimensionless parameter E, which is a measure of the dilatancy of the gouge material due to an increase in strain rate.Earth and Planetary SciencesEngineering and Applied Science

A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band

This paper presents a multiscale analysis of a dilatant shear band using a three-dimensional discrete element method and a lattice Boltzmann/finite element hybrid scheme. In particular, three-dimensional simple shear tests are conducted via the discrete element method. A spatial homogenization is performed to recover the macroscopic stress from the micro-mechanical force chains. The pore geometries of the shear band and host matrix are quantitatively evaluated through morphology analyses and lattice Boltzmann/finite element flow simulations. Results from the discrete element simulations imply that grain sliding and rotation occur predominately with the shear band. These granular motions lead to dilation of pore space inside the shear band and increases in local permeability. While considerable anisotropy in the contact fabric is observed with the shear band, anisotropy of the permeability is, at most, modest in the assemblies composed of spherical grains

Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability

Recent technology advancements on X-ray computed tomography (X-ray CT) offer a nondestructive approach to extract complex three-dimensional geometries with details as small as a few microns in size. This new technology opens the door to study the interplay between microscopic properties (e.g. porosity) and macroscopic fluid transport properties (e.g. permeability). To take full advantage of X-ray CT, we introduce a multiscale framework that relates macroscopic fluid transport behavior not only to porosity but also to other important microstructural attributes, such as occluded/connected porosity and geometrical tortuosity, which are extracted using new computational techniques from digital images of porous materials. In particular, we introduce level set methods, and concepts from graph theory, to determine the geometrical tortuosity and connected porosity, while using a lattice Boltzmann/finite element scheme to obtain homogenized effective permeability at specimen-scale. We showcase the applicability and efficiency of this multiscale framework by two examples, one using a synthetic array and another using a sample of natural sandstone with complex pore structure

Shear heating of a fluid-saturated slip-weakening dilatant fault zone : 2. quasi-drained regime

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Multiscale framework for predicting the coupling between deformation and fluid diffusion in porous rocks

In this project, a predictive multiscale framework will be developed to simulate the strong coupling between solid deformations and fluid diffusion in porous rocks. We intend to improve macroscale modeling by incorporating fundamental physical modeling at the microscale in a computationally efficient way. This is an essential step toward further developments in multiphysics modeling, linking hydraulic, thermal, chemical, and geomechanical processes. This research will focus on areas where severe deformations are observed, such as deformation bands, where classical phenomenology breaks down. Multiscale geometric complexities and key geomechanical and hydraulic attributes of deformation bands (e.g., grain sliding and crushing, and pore collapse, causing interstitial fluid expulsion under saturated conditions), can significantly affect the constitutive response of the skeleton and the intrinsic permeability. Discrete mechanics (DEM) and the lattice Boltzmann method (LBM) will be used to probe the microstructure---under the current state---to extract the evolution of macroscopic constitutive parameters and the permeability tensor. These evolving macroscopic constitutive parameters are then directly used in continuum scale predictions using the finite element method (FEM) accounting for the coupled solid deformation and fluid diffusion. A particularly valuable aspect of this research is the thorough quantitative verification and validation program at different scales. The multiscale homogenization framework will be validated using X-ray computed tomography and 3D digital image correlation in situ at the Advanced Photon Source in Argonne National Laboratories. Also, the hierarchical computations at the specimen level will be validated using the aforementioned techniques in samples of sandstone undergoing deformation bands