Strain Localization In Sand Research Articles

Micromechanics and Strain Localization in Sand in the Ductile Regime

AbstractCritical processes including seismic faulting, reservoir compartmentalization, and borehole failure involve high‐pressure mechanical behavior and strain localization of sedimentary rocks such as sandstone. Sand is often used as a model material to study the mechanical behavior of poorly lithified sandstone. Recent studies exploring the multi‐scale mechanics of sand have characterized the brittle, low‐pressure regime of behavior; however, limited work has provided insights into the ductile, high‐pressure regime of behavior via in‐situ measurements. Critical features of the ductile regime, including grain breakage, grain micromechanics, and volumetric strain behavior therefore remain under‐explored. Here, we use a new high‐pressure triaxial apparatus with in‐situ x‐ray tomography to provide new insights into deformation banding, grain breakage, and grain micromechanics in Ottawa sand subjected to triaxial compression under confining pressures between 10 and 45 MPa. We observed strain‐hardening at pressures above 15 MPa and strain‐neutral responses at pressures below 15 MPa. Compacting shear bands and grain breakage were observed at all pressures with no significant variation due to grain size, except for minor increases in breakage in less‐rounded sands. Grain breakage emerged at stress levels lower than the assumed yield threshold and more intense breakage was associated with thinner deformation bands. Contact sliding at inter‐grain contacts demonstrated a bifurcation into a bimodal distribution, with intense sliding within deformation bands and reduced but non‐negligible sliding outside of deformation bands, suggesting that off‐band zones remain mechanically active during strain hardening.

Strain localization and fabric evolution in sand

Strain localization is frequently observed in sand and is considered an important precursor related to major geohazards such as landslides, debris flow and failure of relevant geo-structures. This paper presents a numerical study on strain localization in sand, with a special emphasis on the influence of soil fabric and its evolution on the initiation and development of shear band. In particular, a critical state sand plasticity model accounting for the effect of fabric and its evolution is used in the finite element analysis of plane strain compression tests. It is found that the initiation of shear band is controlled by the initial fabric, while the development of shear band is governed by two competing physical mechanisms, namely, the structural constraint and the evolution of fabric. The evolution of fabric generally makes the sand response more coaxial with the applied load, while the structural constraint induced by the sample ends leads to more inhomogeneous deformation within the sand sample when the initial fabric is non-coaxial with the applied stress. In the case of smooth boundary condition, structural constraint dominates over the fabric evolution and leads to the formation of a single shear band. When the boundary condition is rough, the structural constraint may play a comparable role with fabric evolution, which leads to symmetric cross-shape shear bands. If the fabric is prohibited from evolving in the latter case, a cross-shape shear band pattern is found with the one initiated first by the structural constraint dominating over the second one. In all cases, significantly larger dilation and fabric evolution are observed inside the shear band than outside. The simulated shear band orientation coincides with the Roscoe’s angle for cases with high confining pressure and lies in between the Roscoe’s angle and Arthur’s angle for the low confining pressure cases.

Strain Localization of Sand Based on a State-Dependent Critical State Model

A state-dependent critical state model is employed to analyze strain localization of sand in this paper. The sand model is developed based on the concept of the state-dependent critical state for sands, and an analysis of strain localization is performed on the drained plane strain tests of Hostun sand. The results show that the state-dependent critical state model is capable of simulating the effect of initial state on strain localization compatibly.

Imaging sand deformation at the grain scale

Shear banding, the localization of deformation into thin zones of intense shearing, is a phenomenon commonly observed in sand and other granular materials. The most valuable experimental contributions to the understanding of shear banding are those measuring, in one way or another, the full field of deformation in the specimen – which is the only means by which test results can be appropriately interpreted [1]. Full-field analysis of strain localization in sand possibly started in the late 1960s in Cambridge and was continued over the last decades in the work of a number of groups, including Grenoble. Most of these works were performed using specifically designed plane strain devices, and used a range of full-field methods, the more advanced of which allowed observation of the specimen throughout loading by optical methods, thereby permitting measurement of the evolving strain field. In the 1960s, x-ray radiography was first used to measure 2D strain fields in sand. From the early 1980s, x-ray tomography was used by a few groups working in geomechanics, including Desrues and coworkers (see [2] for a review). These studies provided valuable 3D information on localization patterning in sand, and also demonstrated the potential of x-ray tomography as a quantitative tool, e.g., for measuring the evolution of void ratio inside a shear band and its relation to critical state. The recent advent of x-ray micro tomography, originally with synchrotron sources and now with laboratory scanners, has provided much finer spatial resolution, which opens up new possibilities for understanding the mechanics of granular media (in 3D) at the scale of the grain. For example, Oda and coworkers [3] presented micro tomography images of sand grains inside a shear band, showing organized structures that would not have been seen in standard x-ray tomography images (because of insufficient resolution) and that had only previously been observed in 2D thin sections. It should be noted that the images by Oda were obtained post-mortem, i.e., after testing. However, a full understanding of the mechanisms of (localized) deformation can only be achieved if the entire deformation process is followed throughout a test while the specimen deforms. This is possible by using in-situ x-ray tomography (in-situ meaning x-ray scanning at the same time as loading). A number of such in-situ studies for triaxial tests on sand were performed over the last ten years or so, mostly using medical or industrial tomography systems, and in a few cases synchrotron micro tomography, which allows identifying individual sand grains and tracking their displacements throughout a test. The aim of the present study is both to observe the material evolution under loading with grainscale resolution and to image the deformation processes. In recent work [4], we applied 3D Volumetric Digital Image Correlation (V-DIC) to a sequence of x-ray tomography images taken during a triaxial test on a clay-rock specimen. In the present paper, we show results of a similar DICbased analysis of deformation for sand specimens under triaxial compression. Two different granular materials were tested: Hostun sand, a fine-grained, angular siliceous sand with a mean grain size (D50) of about 300 m, and Caicos ooid, a material characterized by spheroidal grains with D50 of about 420 m. In addition, we have developed a grain-scale V-DIC method that permits the characterization of the full kinematics (i.e., 3D displacements and rotations) of all the individual © Owned by the authors, published by EDP Sciences, 2010 DOI:10.1051/epjconf/20100622021 EPJ Web of Conferences 6, 22021 (2010)

Numerical simulation of fabric anisotropy and strain localization of sand under simple shear

AbstractThis paper studies the effects of initial fabric anisotropy of dry sand in simple shear deformation. The effects of anisotropy are taken into consideration through the modification of the mobilized friction in the Mohr–Coulomb‐type yield surface as a function of a fabric parameter. In addition, the constitutive model uses a gradient term that directly incorporates the effects of material length scale. The constitutive formulation is implemented into ABAQUS finite element code and used to simulate shearing of the dry sand under various conditions of simple shear. The numerical simulations show that while the shear stress response is affected by fabric anisotropy, its effects on strain localization in simple shear are minimal. This is in contrast to other devices such as the biaxial shear. The strain localization in simple shear is controlled more by the imposed boundary conditions. The use of material length scale is shown to remove the effects of strain localization in the shearing response. Copyright © 2009 John Wiley & Sons, Ltd.

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

AbstractExperimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd

Characterization of failure in sand under triaxial compression using an industrial X-ray CT scanner

A new triaxial compression test apparatus was developed for use with an industrial X-ray computed tomography (X-ray CT) scanner and used to characterize progressive failure with strain localization in sand. Performance of the new triaxial compression apparatus was verified separately prior to use within an X-ray CT scanner system. High quality visualizations obtained from a series of nondestructive tests conducted under triaxial compression with the new test apparatus made it possible to visually characterize progressive failure with propagating strain localization in a soil specimen using three-dimensional CT images. Specifications for the new apparatus and procedures for its use were established and potential applications and avenues of further research were discussed.