Shear Bands In Sand Research Articles

An experimental study on shear bands in sand using the orthogonal cutting setup

We study the evolution of shear bands in granular media subjected to very large deformations using the orthogonal cutting geometry. We perform our cutting experiments on Cauvery Delta sand with d50 of 0.45mm. We also capture images of the cutting process which allows us to perform a PIV analysis to determine the deformation in material around the cutting tool. In our experiments we observe that the dynamic angle of repose of the pile that forms in-front of the tool as cutting progresses, approaches the critical state friction angle of the material. We observe a flow bifurcation around the tool as the material begins to slip along planes which are oriented at an angle of π/4 – θ/2, θ being the dynamic angle of repose, to the cutting direction. This leads to formation of shear bands/velocity jumps which contain around 14 particles. A measurement of dilation angle within the shear bands indicate that material is in a critical state of deformation.

The Role of Deformation Bands in Dictating Poromechanical Properties of Unconsolidated Sand and Sandstone

AbstractCataclastic shear bands in sands and sandstones are typically stronger, stiffer, and exhibit lower permeability than the surrounding matrix, and therefore act as barriers to fluid flow. Previous work has quantified the reduction in permeability associated with these features; however, little is known about the role of shear band structure in controlling the way they impact permeability and elastic properties. Here, we report on a suite of laboratory measurements designed to measure the poromechanical properties for host material and natural shear bands, over effective stresses from 1–65 MPa. In order to investigate the role of host material properties in controlling poromechanical evolution with stress, we sampled shear bands from two well‐studied sandstones representing structurally distinct end‐members: a poorly cemented marine terrace sand from the footwall of the McKinleyville thrust fault in Humboldt County, California, and a strongly‐cemented sandstone from the hanging wall of the Moab Fault in Moab, Utah. The permeability‐porosity trends are similar for all samples, with permeability decreasing systematically with increasing effective stress and decreasing porosity. The permeability of the host material is consistently >1 order of magnitude greater than the shear bands for both localities. For the unconsolidated case, shear bands are less permeable and stiffer than the host material, whereas for the consolidated case, shear bands are slightly less permeable, and wave speeds are slower than in the host. We attribute the differences between the McKinleyville and Moab examples to changes in structure of the nearby host material that accompanied formation of the shear band.

Bifurcation prediction of shear banding in sand with non-coaxial critical state model considering inherent anisotropy

In view of phenomenological observations, the anisotropic state variable accounting for the effect of inherent fabric anisotropy, which can describe the microstructural characteristics of sand, is thought to influence the critical state of sand. Based on revised forms of the anisotropic state variable, the form for the anisotropic critical state line function is revised and the non-monotonically anisotropic effects are incorporated into the strength parameter in the re-adjustment of the elements of the model. The anisotropic plasticity model parameters of Toyoura sand are re-calibrated with triaxial compression and extension tests having various deposition directions. In comparison to the experiments on Toyoura sand, it is shown that the model can simulate the anisotropic stress-strain relationship reasonably well. Then, bifurcation analyses are conducted to predict the onset of strain localization with the corresponding non-coaxial anisotropic model. The results show that the modeling of shear band formation based on the non-coaxial model is in agreement with the tests considering the anisotropic characteristic.

All you need is shape: Predicting shear banding in sand with LS-DEM

This paper presents discrete element method (DEM) simulations with experimental comparisons at multiple length scales—underscoring the crucial role of particle shape. The simulations build on technological advances in the DEM furnished by level sets (LS-DEM), which enable the mathematical representation of the surface of arbitrarily-shaped particles such as grains of sand. We show that this ability to model shape enables unprecedented capture of the mechanics of granular materials across scales ranging from macroscopic behavior to local behavior to particle behavior. Specifically, the model is able to predict the onset and evolution of shear banding in sands, replicating the most advanced high-fidelity experiments in triaxial compression equipped with sequential X-ray tomography imaging. We present comparisons of the model and experiment at an unprecedented level of quantitative agreement—building a one-to-one model where every particle in the more than 53,000-particle array has its own avatar or numerical twin. Furthermore, the boundary conditions of the experiment are faithfully captured by modeling the membrane effect as well as the platen displacement and tilting. The results show a computational tool that can give insight into the physics and mechanics of granular materials undergoing shear deformation and failure, with computational times comparable to those of the experiment. One quantitative measure that is extracted from the LS-DEM simulations that is currently not available experimentally is the evolution of three dimensional force chains inside and outside of the shear band. We show that the rotations on the force chains are correlated to the rotations in stress principal directions.

Micro-texture and petrophysical properties of dilation and compaction shear bands in sand

We have studied micro-textural and petrophysical properties of dilation and compaction shear bands (zones) created during deformation of two quartz sands (Ottawa and Hostun sands), differing in angularity, under triaxial compression experiments. Image processing of in-situ CT-scan images taken during the experiments allowed both qualitative study of micro-texture, and quantitative study of porosity and dilatancy. Our results indicate that, in both sands at low confining pressure, i.e. 100 kPa, a zone of enhanced porosity (dilation shear band) is initiated with dilatancy factor ∼0.5–0.6, and towards the end of the tests the porosity continuously increases, especially at the center of the zone (from ∼33% to ∼45% for Ottawa sand and from ∼40% to ∼52% for Hostun sand). However at high confining pressure (7000 kPa), the tested sands reveal different dilatancy and porosity evolution. In rounded Ottawa sand, first a wide dilated zone (dilatancy factor ∼0.26) forms, and by progressive shear loading, a compacted zone is developed inside this dilated zone (dilatancy factor ∼−0.11). For the angular Hostun sand the dilatancy is negative both at the initiation and the final stage, which is reflected by a wide zone of compaction.

The microstructure and internal architecture of shear bands in sand–clay sequences

The microstructures of cm-scale displacement faults offsetting unlithified sequences of finely interbedded sands, silts and clays from outcrops in Denmark have been examined. A variety of shear band types are recognised based on their grain-scale deformation mechanism and internal structure. Shear bands in a Jurassic sequence exposed along the coastline of Bornholm are characterised by intense cataclasis of both sand and clay layers. This deformation mechanism is accompanied by extensive grain scale mixing along discrete shear bands to give a fault rock composition that reflects the relative amount of sand and clay within the faulted sequence. In contrast, shear bands at Nr. Lyngby and Jensgaard, both on the Jutland coast, are characterised by granular flow within the sand units. Grain scale mixing is subdued at these locations so that layers maintain their integrity across the shear band to form a layered internal structure of sand, silt and clay smears. In some instances, particularly at Nr. Lyngby, clays have deformed in a brittle manner so that they do not contribute material to the shear band, which is then comprised exclusively of coarser-grained components. The different deformation mechanisms and internal structures of shear bands are thought to be controlled by burial depth at the time of faulting.

Characterization of mesoscale instabilities in localized granular shear using digital image correlation

Within shear bands in sands, deformation is largely non-affine, stemming primarily from buckling of well-known force chains and also from vortex-like structures. In the spirit of current trends toward multiscale modeling, understanding the links between these mesoscale deformational entities and corresponding macroscale response will form the basis for the next generation of sand behavioral models and may also aid in efforts to understand jamming–unjamming transitions in dense granular flows in general. Experimental methods to quantify and characterize such subscale kinematics, in particular in real sands, will play critical roles in these efforts. Digital Image Correlation (DIC) is a fast growing experimental technique to nondestructively measure surface displacements from digital images. Here, DIC has been employed to identify and characterize the development of vortex structures inside shear bands formed in dense sands during plane strain compression. A rigorous assessment of the DIC method has been performed, in particular for subscale behavioral characterization in unbonded granular solids, and guidelines are offered for accurate implementation. While DIC systematically overestimates shear band thickness, a methodology has been devised to compensate for this overestimation. Shear band thickness for four different uniform sands were found to range between 6 and 9 grain diameters, and for a well-graded sand between 8 and 9.5 grain diameters. These determinations agree with visual inspections of grain kinematics from the image data, as well as recent theoretical predictions.

Finite strain analysis of nonuniform deformation inside shear bands in sands

SUMMARYA methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian‐based large‐strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain‐scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening‐critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size. Copyright © 2011 John Wiley & Sons, Ltd.

Evolution of force chains in shear bands in sands

Precise knowledge of the post-peak constitutive response occurring within shear bands in sands is of keen interest in geomechanics, particularly for accurate modelling of progressive failure phenomena. There is mounting evidence that the displacement field within shear bands in sands is non-uniform and distinguished by distinct meso-scale features: namely, particle force chains. Experimental validation of such features will help elucidate the precise nature of the deformation field within shear bands. This paper presents experimental evidence of the kinematic signatures of force chain activity within shear bands in sands. The meso-scale kinematics are quantified from digital-image-correlation-based, grain-scale displacement analyses performed on digital images of specimens undergoing plane strain compression. As in previous work, the data reveal distinct, systematic patterns in the kinematics along the length of the shear band, which serve as indirect evidence of force chain build-up and collapse. Herein, local volume changes are shown to integrate into this pattern. Temporal changes in these patterns with the progress of deformation are also tracked. It is argued that the changes observed in the kinematics from softening to critical state provide a physical, meso-scale explanation for the progress of global stress–strain response through the post-peak regime.

Professor Ioannis Vardoulakis (1949–2009)

Professor Ioannis Vardoulakis (1949–2009)

Multiscale investigation of shear bands in sand: Physical and numerical experiments

AbstractIn many geotechnical systems, it is not uncommon to observe failure in zones of high localized strain called shear bands. The existing models predict the existence and the extent of these localizations, but provide little insight into the micromechanics within the shear bands. This research captures and compares the variation in microstructure both inside and outside of shear bands that formed in physical laboratory plane strain and companion numerical two‐dimensional discrete element method (DEM) biaxial compression experiments. Unsheared and sheared laboratory specimens of Ottawa 20–30 sand of varying dilatancy were solidified using a two‐stage resin impregnation procedure. The solidified specimens were sectioned and the resulting surfaces were prepared for microstructure observation using optical bright‐field microscopy and stereological analysis. Statistical properties of microstructural parameters for sub‐regions in a grid pattern and along predefined inclined zones were determined. Similar measurements were performed on 2D DEM simulation specimens at varying strain levels to characterize the evolution of microstructure with increasing strain. The results showed how differences evolved in the mean, standard deviation, and entropy of void distributions with increasing global strain levels. The results indicate how disorder increases and that the material within the shear band does not adhere to the classical concept of critical state, but reaches a terminal void ratio that is largely a function of initial void ratio. Furthermore, there appears to be a transition zone between the far field and the fully formed shear block, as opposed to an abrupt delineation as is traditionally inferred. Copyright © 2010 John Wiley & Sons, Ltd.

Prediction of shear bands in sand based on granular flow model and two-phase equilibrium

In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics, shear bands in sand are considered as high-strain phase (plastic phase) of sand and the materials outside the bands are still in low-strain phase (elastic phase), namely, the two phases of sand can coexist under certain condition. As a one-dimensional example, the results show that, for materials with strain-softening behavior, the two-phase solution is a stable branch of solutions, but the method to find two-phase solutions is very different from the one for bifurcation analysis. The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens, discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered, the continuity of displacements and traction across interfaces is imposed, and the Maxwell relation is satisfied. The governing equations are deduced. The critical stress for the formation of a shear band, both the stresses and strains inside the band and outside the band, and the inclination angle of the band can all be predicted. The predicted results are consistent with experimental measurements.

Centrifuge Modeling of Granular Soil Response Over Active Circular Trapdoors

The trapdoor problem is a useful model for providing a clearer understanding of stress distribution around basic geotechnical engineering structures such as tunnels, conduits and anchor plates. The interest is mainly directed towards the determination of soil load on the trapdoor, which can be substantially different from the initial geostatic loads, when the trapdoor is moved even slightly. Development of shear bands around the yielding trapdoor is also of interest. A series of centrifuge and 1g model tests were conducted to study active arching in dry granular soil on circular trapdoors. The study was undertaken mainly because of two reasons: (i) limited success in earlier centrifuge modeling studies of a trapdoor problem, and (ii) a lack of understanding of the load-displacement characteristics under axisymmetric conditions. A trapdoor assembly and in-flight precompression technique were developed to perform a series of tests involving different overburden soil thickness on circular doors of different diameters. Correct initial geostatic loads were measured. Greater confidence in the experimental results was obtained because modeling of models type experiments were also successful. A parametric study involving different overburden soil thickness to trapdoor diameter ratios (H/D) ranging from 0.67 to 6 was conducted. The pattern of shear bands in sand above the trapdoor observed in a centrifuge model under a high gravity field differed considerably from that in a 1g model. Maximum arching was completely mobilized at movements of only 1.5% of trapdoor diameter. The minimum load on the trapdoor became constant at H/D equal to 5 regardless of the initial overburden pressure or height of the soil model.

Evolution of shear bands in sand

Localisation of deformation in narrow shear bands is a fundamental phenomenon of granular material behaviour. When modelling granular materials, shear localisation has therefore to be considered. The model must include an adequate constitutive law with an intrinsic length determining the thickness of the localised shear zones, and a representation of microscopic inhomogeneities triggering shear localisation. In the framework of a Cosserat continuum the behaviour of non-cemented granular material can be described by a hypoplastic law including the evolution of non-symmetric stresses and couple stresses. Void ratio fluctuations are introduced by a physically justified probability density function. The assumption is that fluctuations are minimal in the densest state, and maximal in the critical state. It is shown that shear bands can evolve spontaneously in the interior of a granular body even under homogeneous stress or displacement boundary conditions. Experimental verifications are given. Numerical results are compared with laboratory tests performed with a Cornforth and a Hamblytype biaxial apparatus. Shear localisation in the experiment is visualised by means of an optical method called particle image velocimetry. Further numerical results are compared with experimental results taken from publications.

Evolution of shear bands in sand

Evolution of shear bands in sand

Use of Stereophotogrammetry to Analyze the Development of Shear Bands in Sand

Abstract Experimental results are presented from plane-strain compression of a fine-grained, water-saturated loose sand. Together with local measurements of boundary stresses and deformations, systematic analysis of photographs of the deforming specimen allowed for measuring deformations and computing strain fields inside and outside the shear band. The principles, details, and accuracy of the procedure are described. The capabilities of stereophotogrammetry are illustrated through typical results obtained from undrained and drained tests. A gradual transition from homogeneous deformation to temporary modes of localized strain to a highly localized strain field is systematically observed. Prior to strain localization in the region where the final shear band eventually forms, the soil contracts more than the rest of the specimen. As soon as the final band is fully formed, the soil inside the band either remains at constant volume or dilates. The nonuniformity of volumetric response throughout the specimen in globally undrained conditions implies there is water flow within the specimen.