The Relationship between Damage and Localization

Edited by H. Lewis and G. D. Couples


The many kinds of porous geomaterials (rocks, soils, concrete, etc.) exhibit a range of responses when undergoing inelastic deformation. In doing so they commonly develop well-ordered fabric elements, forming fractures, shear bands and compaction bands, so creating the planar fabrics that are regarded as localization. Because these induced localization fabrics alter the bulk material properties (such as permeability, acoustic characteristics and strength), it is important to understand how and why localization occurs, and how it relates to its setting. The concept of damage (in several uses) describes both the precursor to localization and the context within which it occurs. A key theme is that geomaterials display a strong material evolution during deformation, revealing a close linkage between the damage and localization processes.

This volume assembles perspectives from a number of disciplines, including soil mechanics, rock mechanics, structural geology, seismic anisotropy and reservoir engineering. The papers range from theoretical to observational, and include contributions showing how the deformed geomaterials' emergent bulk characteristics, like permeability and seismic anisotropy, can be predicted. This book will be of interest to a wide range of geoscientists and engineers who deal with characterization of deformed materials.

  1. Page 1

    The papers that appear in this Special Publication were assembled to address a topic that was the subject of a conference entitled ‘Damage and Localization’, one of a series of three Euroconferences on rock mechanics and rock physics that were supported by European Commission funding. Some of papers contained herein were derived from the contributions presented at that meeting, but others were solicited subsequently in order to create a coherent volume that illustrates some key facets of the topic as it is now understood. However, the subject is sufficiently broad that a single collection of papers cannot hope to do justice to the whole theme. This Introduction outlines the conceptual threads that underpin the selection of papers that are included in this volume and introduces the cross-scale relationships that are addressed by the individual contributons. We hope that the reader will find these contributions to be stimulating and informative.

  2. Page 7

    In upper crustal conditions (the brittle field), rocks subjected to a load can experience a deterioration of physical and mechanical properties. This paper treats two conceptual approaches to model the deterioration that results from a crack distribution, whether the distribution is more or less diffuse or is strongly localized. The first part deals with possible ways to characterize diffuse microcracking (damage) to establish how the elastic response reflects the microcracking. This is of direct geophysical interest, as elastic wave velocities carry quantitative information on crack content. The second part summarizes two kinds of theory to predict the failure by crack propagation or strain localization, using either fracture mechanics or bifurcation theory. This is of direct geomechanical interest, as what is looked for is an interpretation of localized structures. The third part presents the complementarities between both concepts, damage and localization, to predict failure in rocks.

  3. Page 19

    Excellent quarry exposures have been studied to examine the controls on the growth of fault networks in Cretaceous high-porosity sands. An inverse correlation is found at any one locality between the frequency of faults of an earlier tectonic event and the frequency of later faults. The early faults are cataclastic deformation bands with displacements typically up to 300 mm, and have thicknesses approaching their displacements. Later faults are also deformation bands except where present within a high-frequency array of earlier faults, where they are typically clustered high-displacement ultracataclasite zones that are narrower (smaller width/displacement ratios) than for the deformation band faults. A mechanical model using critical state soil mechanics explains the observed distributions and fault zone characteristics in terms of strength changes in the deforming sand unit and the stress path by which the material is subjected to ‘clastic’–plastic yielding. Localized faulting by constant-volume cataclastic flow at the critical state line will result in deviatoric stress reduction as Coulomb plasticity softening occurs within the fault zone. Elastic unloading of the walls will suppress the continued formation of deformation bands. The point at which the stress state reaches the critical state line, governed by the stress state and position of the ‘clastic’–plastic yield envelope, is therefore crucial in controlling the final distribution of deformation bands and larger faults in the system. Within this framework, the field and microstructural data suggest that earlier deformation became distributed by hardening processes such as compaction and grain-size reduction, resulting in a higher bulk yield strength. In a later tectonic event, the unit behaves in a stronger manner and deformation quickly localizes by fault zone softening processes into fewer fault zones that individually grow larger.

  4. Page 47

    The main purpose of this paper is a broad review of developments in observation and interpretation of localization in geomaterials in the laboratory, with an emphasis on low mean stress situations. Laboratory investigation of strain localization in granular soils and rocks has been pursued extensively and very accurate strain field evolution measurement techniques have been developed, including false relief stereophotogrammetry (FRS) and computed tomography (CT). These permit full characterization of strain localization, from onset to complete shear band formation. This paper reviews studies of sand, clay, sandstone, stiff marl and concrete, and observations of incipient and developed localization in initially ‘homogeneous’ laboratory tests are presented. Development of localization and peak strength, critical stress and strain, shear band orientation and thickness, and complex localization patterns are discussed. Deformation during triaxial compression of sand is shown to develop complex strain localization patterns. Consequently, the critical void ratio concept in granular materials is reconsidered. Void ratio evolution, global and local, monitored by CT, shows a limiting void ratio being rapidly attained in the strain localization zones. In cohesive materials (clays, rocks and concrete), crack development is also commonly observed. Displacement discontinuity measurement techniques are presented and the results for different cohesive geomaterials are discussed.

  5. Page 75

    Laboratory experiments suggest that fault zones form in porous rocks through the extension and coalescence of fractures of predictable geometries. These fractures form in an array of Riedel fractures in R1, R2, P and Y orientations. Displacement along closely spaced fractures leads to the formation of comminuted fault gouge. Localization of displacement within the fault gouge progresses from distributed shearing to comminution and compaction of the fault rock material culminating in fractures in the Riedel orientations. Colour boundaries within the simulated gouge zones show the change in accommodation of displacement to fractures in the Y orientation as shear strain progresses. Clay–quartz mixtures demonstrate that the clay inhibits localization and the achievement of steady-state sliding as well as stick-slip. A reduction in the coefficient of friction does not occur until about 30% of the clay is present and continues to decrease until about 70% is reached. Localization of slip appears as a necessary condition for steady-state sliding as well as unstable behaviour. Field studies show the implication of grain-size reduction in the localization process by porosity decrease inhibiting fluid flow normal to the fault zone. The pervasive Y fractures, however, facilitate fluid migration parallel to some faults.

  6. Page 89

    Recent field, laboratory, and theoretical studies suggest that under certain stress conditions, compaction of porous rock may be accommodated by narrow zones of localized compressive deformation oriented perpendicular to the maximum compressive stress. Triaxial compression experiments were performed on Castlegate sandstone, an analogue reservoir sandstone, that included acoustic emission detection and location. Initially, acoustic emissions were concentrated in horizontal bands that initiated at the sample ends (perpendicular to the maximum compressive stress) but, with continued loading, progressed axially towards the sample centre. High-resolution field-emission SEM was performed to elucidate the micromechanics of compaction. The microscopy revealed that compaction of this weakly cemented sandstone proceeded in two phases: an initial stage of porosity decrease accomplished by breakage of grain contacts and grain rotation, and a second stage of further porosity reduction accommodated by intense grain breakage and rotation. Quantitative stereological measurements corroborated the decrease in the intergrain spacing and the increase in grain boundary contacts that the microstructural observations suggest occurred during the first stage of compaction. The microstructural data show that a five-fold increase in the surface area per unit volume resulted from the extensive microfracturing that occurred during the second stage of compaction.

  7. Page 105

    To investigate the interaction between the rheology of arenaceous sedimentary rocks (sand and sandstone) and stress conditions during burial we have coupled published results from deformation experiments with a simple quartz cementation model. The model provides valuable insights into controls on sandstone deformation consistent with observations from nature. A transitional zone exists in subsiding sedimentary basins, here referred to as the ductile-to-brittle transition (DBT), above which faults in normally pressured arenites will tend to form fluid flow barriers, and below which they will tend to form conduits. The DBT depth in sandstone is dependent upon geothermal gradient, burial rate and grain size. Low geothermal gradients, rapid sedimentation rates and coarse grain sizes favour a deep DBT and vice versa. Fine-grained arenites may only deform in a brittle manner for most natural burial rates and geothermal gradients, explaining why they do not usually contain thick deformation band zones. Coarser-grained arenites may deform in a brittle–ductile or ductile manner, which is why they often contain thick deformation band zones and occasionally experience pervasive porosity collapse. Sandstones within high geothermal gradient areas may deform to produce fluid flow conduits at shallow depths when porosities in the sequence as a whole are high; this possibly favours fault-related mineralization.

  8. Page 123

    Fracture mechanics modelling of fracture pattern development was used to analyse pattern geometry and population statistics for natural opening-mode fractures. Orthogonal fracture network geometries were generated under biaxial extension loading conditions from a slightly anisotropic initial strain state. Fracture statistics were analysed by grouping all fracture orientations into one population for these unique orthogonal pattern geometries. Fracture aperture distributions resembled negative exponential curve shapes, consistent with published observations for stratabound fractures in sedimentary rock. Fracture length distributions had a strongly power-law shape, and showed that longer fractures grew first and reached their fullest extent before shorter fractures began propagating. The power-law shape of the length distribution was first established by the growth of the longest fractures in the population, followed by the later growth of shorter fractures that extended the power-law shape to smaller sizes. The shortest fracture length at which the power-law distribution was truncated varied with the magnitude of the applied strain. Other variations in fracture pattern results were tied to mechanical layer thickness and subcritical crack growth propagation properties of the fractured media.

  9. Page 143

    We describe laboratory measurements of the permeability of fault rocks and their host protoliths obtained from the Median Tectonic Line (MTL), the largest strike-slip fault in Japan. The measurements are made using a gas-medium apparatus that simulates in situ conditions. Samples of fault gouge, cataclastic mylonite, and protoliths were collected from the Kitagawa and Ankoh outcrops of the MTL and adjacent areas in Ohshika-mura, Nagano Prefecture, central Japan. Permeabilities of these samples were measured at room temperature under dry conditions, with nitrogen as the pore fluid. Most samples from the incohesive fault zone have a permeability ranging between 10−13 and 10−17 m2 (100–0.01 mD). These permeabilities are greater than those of cemented cataclasites and mylonites by more than two orders of magnitude at all effective pressures (Pe) up to 180 MPa. Clayey fault gouge material has a permeability as low as 10−19 m2 (0.1 µD) at high effective pressures, but such impermeable fault gouge does not constitute a continuous zone on the two outcrops we studied. Permeability of the incohesive fault rocks exhibits large hysteresis upon Pe cycling, compared with cataclasite and mylonite, because those cemented, cohesive fault rocks undergo much less inelastic deformation during the pressure cycling.

  10. Page 161

    An elastic–plastic material model, with strain-hardening or -softening, and volumetric strains, implemented within a general-purpose finite-element system (SAVFEMTM), is shown to reproduce the stress–strain relationships and localized to de-localized (brittle to ductile) changes in strain response that have long been observed in typical laboratory experiments on common porous rocks. Based on that validation of the implementation, SAVFEMTM is then used to create numerical simulations that reproduce the patterns of localized shear zones, and their growth history, that occur in experimental (physical) models of fold–fault systems in layered rocks. These simulations involve a progressive evolution of the mechanical state, illustrating a geometrically dominated type of localization behaviour. Part of the deformation simulated here represents a crestal graben system. Analysis of the evolving mechanical state in the system of simulated faults poses challenges to some longstanding ideas concerning the way that faults operate, suggesting the need for a new fault-process paradigm.

  11. Page 187

    Predicting deformation-driven permeability changes in the subsurface requires knowledge of the character and distribution of dilatant and compactant rock damage. Seismic reflection data can be used to gain insight into aspects of the deformation such as the geometry of seismically resolvable faults and bulk material property distributions. However, interpretations of material properties from seismic data are non-unique. This paper addresses the use of established seismic techniques to identify the signatures of fault-associated open fractures, modified and improved by a new linked geomechanics–seismic approach. The paper also addresses how each of stress state and open fractures affect seismic anisotropy. The geomechanics–seismic approach is demonstrated using a model of a North Sea hydrocarbon field in which a series of potential fracture arrays are assumed and the fracture apertures are modified to reflect the geomechanically generated stress states. Seismic anisotropy predictions based on these modified fracture distributions are then compared with a pre-existing seismic anisotropy interpretation to determine the best match. Using geomechanical simulation to support a seismic anisotropy-based method produces a higher-confidence result and can lead to better prediction of altered permeabilities in faulted regions. Because of the geomechanical focus of this Special Publication, the background for seismic identification of faults and inter-fault damage is also outlined, including a review of current seismic practice.

  12. Page 209

    Simulation of coupled dynamic fluid flow and geomechanical loading of fractured systems shows that complex behaviours can result, even for geometrically simple fracture systems and simple loading. Using a bi-directionally coupled simulation tool, HYDRO–DDA, we examine how fluids and discontinuum processes interact in a fractured, porous rock layer that is being flexed. The changes in fracture aperture, and hence the equivalent permeabilities of this system, exhibit marked localization or delocalization responses in spite of the geometrical and mechanical simplicity of this model. Typically the linked flow-deformation behaviour develops markedly non-linear responses. In some cases the permeability varies by more than three orders of magnitude for minor changes in input variables. Upscaling methods that are suitable representations of this permeability variation are developed. These non-linear behaviours develop in a porous material, which would be expected to suppress non-linear effects. If the range of behaviours seen in this geometrically simple coupled system is typical of other, potentially more complex, fully coupled systems, then the results obtained here can be used to explain the spatially and temporally high variability of the permeability characteristics of fractured systems.

  13. Page 227

    Current models of lithospheric deformation that involve the concept of proximity to a critical point in its statistical mechanical sense are reviewed in the context of implications for fluid flow in hydrocarbon reservoirs. The data from hydrocarbon fields that support the applicability of this concept are listed. In particular, spatial and temporal correlations of fluctuations in oilfield production and injection rates are assessed. The long-range spatial characteristics of these correlations provide strong support for the reservoirs being close to a point of criticality, at least during their development lifetimes. The implications for reservoir simulation modelling, data acquisition and future research to further elucidate this area are outlined.

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