The localized deformation is a ubiquitous phenomenon in geomaterials It occurs over a vast range of size scales, from the microscale level of grains to faults extending over hundreds of kilometers It occurs in a variety of forms: a concentration or coalescence of cracks; a distinct, planar frictional surface; a gouge zone of finely comminuted material; or simply a region of higher shear strain In geomaterials, the severe shearing in regions of localized deformation may be accompanied by dilatancy (inelastic volume increase) or compaction (inelastic volume decrease) and by chemical alteration Localization can even occur purely by compaction without any evident shear If the material is fluid-saturated, as is frequently the case, inelastic volume changes can induce the flow of fluid or changes in pore pressure that affect the response Localization occurs under a variety of conditions Although most often associated with the formation of shear bands or faults under nominally brittle conditions, localization can also occur by cataclastic flow of rocks at higher mean stresses and by ductile shearing at temperatures and pressures typical of depths of 10 km to 15 km in the earth's crust

Chapter 5 Localization: Shear bands and compaction bands

This chapter reviews and extends analyses of diffusive instabilities in inelastically deforming geomaterials. The onset of these instabilities is connected with the conditions for shear localization in the limiting cases of drained (constant pore pressure) and undrained (constant fluid mass) deformation and depends on whether inelastic volume change is dilation or compaction. Rice [1975] showed that homogeneous shear deformation of a layer was stiffer for undrained than for drained conditions but was unstable in the sense that the magnitude of infinitesimal spatial nonuniformities begins to grow exponentially in time when the condition for localization is met in terms of the underlying drained response. As the condition for localization in terms of the undrained response is passed, infinitesimal spatial perturbations experience infinitely rapid decay and then infinitely rapidly growth. For materials that dilate with inelastic shearing the condition for localization is met for the drained response before it is met for the undrained response. For materials that compact and for which the shear yield stress increases with normal stress, the undrained response is softer than the drained and conditions for localization are met for undrained response before drained. If the shear yield stress decreases with normal stress, as for materials modeled by a “cap” on the yield surface, results for compacting materials are identical to those for the dilating materials. Generalization of the layer results to arbitrary deformation states reveals the same relation for the onset of diffusive instability: spatial nonuniformities begin to grow exponentially when the condition for localization is met in terms of the underlying drained response. In contrast to the result for the layer, the growth rate of perturbations does not necessarily become unbounded when the condition for localization is met in terms of the undrained response. The difference is due to a lack of symmetry in the constitutive tensors that is typical of geomaterials. Explicit expressions are given for the undrained response in terms of the drained for an elastic-plastic relation with yield stress and flow potential depending on first and second stress invariants. For this relation and the limit of incompressible solid constituents, the lack of symmetry just-mentioned disappears. If the fluid constituent is also incompressible, the analysis confirms a result of Runesson et al. [1996] that the undrained response is independent of mean stress and the predicted direction of shear bands is 45° to the principal axes of stress.

/pdf/diffusive-instabilities-in-dilating-and-compacting-lm4et74q95.pdf

Diffusive Instabilities in Dilating and Compacting Geomaterials

This review article discusses the applications of poroelasticity to the mechanics of faulting and failure in geomaterials. Values of material parameters inferred from laboratory and field studies are summarized. Attention is focused on solutions for shear dislocations and shear cracks. A common feature is that undrained response, invoked by rapid slip or deformation, is stiffer than drained response, which occurs for slower slip or deformation. The time and spatial variation of the stress and pore pressure is different for slip on permeable and impermeable planes. These solutions are applied to interpretation of water well level changes due to slip, earthquake precursory processes, and stabilization of spreading slip zones. Inclusion models for reservoirs, aquifers, and other inhomogeneities are formulated and the results are applied to stress and strain changes caused by fluid mass injection or withdrawal. This article has 120 references. @DOI: 10.1115/1.1410935# The shallow parts of the earth’s crust are mostly infiltrated by fluids and the coupling of fluid flow with deformation of the crust alters the response. In particular, this coupling introduces a dependence on time into the response, in addition to any time-dependence of the solid matrix itself. Deep drill holes have encountered significant quantities of fluid at surprisingly large depths, nearly 10 km @1,2#, and geochemical analysis of fluids associated with the faults in California @3# suggest that the fluids originated from the mantle. Consequently, this coupling may be a significant effect not only at shallow depths but throughout the crust.

/pdf/coupled-deformation-diffusion-effects-in-the-mechanics-of-21kerd68ne.pdf

Coupled deformation-diffusion effects in the mechanics of faulting and failure of geomaterials

Several three-dimensional effects were observed in the performance monitoring data collected during excavation for the Ford Engineering Design Center in Evanston, Illinois. The elevations of the soil around the excavation varied and the excavator removed the soil in a nonuniform excavation process, both of which contributed to the observed three-dimensional (3D) effects. This paper describes the excavation support system and subsurface conditions at the site, summarizes the construction procedures, and presents the lateral soil movements measured by inclinometers, ground-surface movements measured by an automated total station, tilt of components of an adjacent structure, and forces in internal braces. These responses are compared with expected responses from current design methods. The 3D nature of the excavation resulted in smaller movements on the side of the excavation, where the retained soil was lowest, an unexpected pattern of axial strut loads and very slight damage to an exterior wall that paralleled one of the excavation walls.

Three-Dimensional Responses Observed in an Internally Braced Excavation in Soft Clay

Coupled deformation-pore fluid diffusion effects on the development of localized deformation in fault gouge

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Coupled deformation-pore fluid diffusion effects on the development of localized deformation in fault gouge