Finite strain analysis of nonuniform deformation inside shear bands in sands

A 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.     

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.     

减围压平面应变压缩试验条件下丰浦砂中剪切带特性研究

不同于常规土体单元试验中恒定围压的应力路径,进行了减围压（卸载）应力路径下丰浦砂的平面应变压缩试验,研究了初始围压和初始相对密度对砂土的剪切强度和剪切带特性的影响。结合二维数字图像（DIC）相关方法,分析剪切带的形成过程,对剪切带的厚度和倾角及其影响因素进行定量地分析。研究结果表明,剪切带形成于峰值剪切强度之前;对于密实丰浦砂试样,随着围压的增加,其剪切强度(最大有效主应力比)减小且峰值强度出现越晚,剪切带厚度减小而剪切带倾角变化不大;丰浦砂试样的相对密度越高,剪切强度越大且峰值强度出现越早,剪切带厚度越小而剪切带倾角越高。此外,基于峰值内摩擦角的Coulomb公式可以较好地预测平面应变试验条件下丰浦砂的最大剪切带倾角。     

Changes in permeability of sand during triaxial loading: effect of fine particles production

Various mechanisms can affect the permeability of dense unconsolidated sands: Volumetric dilation can lead to permeability increase, whereas strain localization in shear bands may increase or decrease the permeability depending on the state of compaction and on the level of grains breakage inside the band. To investigate these various mechanisms, an experimental study has been performed to explore the effect of different factors such as grain size and grain shape, confining pressure, level of shear, stress path, and formation of one or several shear bands on the permeability of dense sands under triaxial loading. The experimental results show a reduction of permeability during the consolidation phase and during the volumetric contraction phase of shear loading, which can be related to the decrease of porosity. The experimental results also show that, depending on the confining pressure, the permeability remains stable or decreases during the volumetric dilation phase despite the increase of total porosity. This permeability reduction is attributed to the presence of fine particles, which result from grains attrition during pre-localization and grains breakage inside the shear band during the post-localization phase.     

A model of strain localization in porous sandstone as a function of tectonic setting,burial and material properties; new insight from Provence (southern France)

The analysis of three cataclastic band sets from Provence (France) reveals that the band density, their conjugate angles, their ratio of shear displacement to compaction, and the amount of cataclasis within the bands differ and can be expressed as functions of tectonic setting and petrophysical properties. We identify (1) a dense and closely spaced network of shear-enhanced (reverse) compaction bands; (2) a regularly spaced less dense network of reverse compactional shear bands; and (3) a localized network of normal shear bands. The field data show that strain localization is favored in an extensional regime and is characterized by shear bands with a large shear to compaction ratio and a small conjugate band angle. In contrast, distributed strain is favored in a contractional regime and is characterized by compactional bands with a low ratio of shear to compaction and a large conjugate band angle. To explain the mechanical origin of this strain localization, we quantify the yield strength and the stress evolution in extensional and contractional regimes in a frictional porous granular material. We propose a model of strain localization in porous sands as a function of tectonic stresses, burial depth, material properties, strain hardening and fluid pressure. Our model suggests that stress reduction, inherent to extensional regime, favors strain localization as shear bands, whereas stress increase during contraction favors development of compactional bands.     

Random porosity fields and their influence on the stability of granular media

It is well established that the mechanical behavior of granular media is strongly influenced by the media's microstructure. In this work, the influence of the microstructure is studied by integrating advances in the areas of geostatistics and computational plasticity, by spatially varying the porosity on samples of sand. In particular, geostatistical tools are used to characterize and simulate random porosity fields that are then fed into a nonlinear finite element model. The underlying effective mechanical response of the granular medium is governed by a newly developed elastoplastic model for sands, which readily incorporates spatial variability in the porosity field at the meso‐scale. The objective of this study is to assess the influence of heterogeneities in the porosity field on the stability of sand samples. One hundred and fifty isotropic and anisotropic samples of dense sand are failed under plane‐strain compression tests using Monte Carlo techniques. Results from parametric studies indicate that the axial strength of a specimen is affected by both the degree and orientation of anisotropy in heterogeneous porosity values with anisotropy orientation having a dominant effect, especially when the bands of high porosity are aligned with the natural orientation of shear banding in the specimen. Copyright © 2007 John Wiley & Sons, Ltd.     

单粒组密砂剪切带的直剪试验离散元数值分析

为分析砂土的剪切力学特性,采用离散元商业软件PFC2D对单粒组密砂在直剪试验中出现的剪切带进行了数值分析。改进传统的分条带观察方式,采用矩形格分割法观察试样内部不同区域的变形特性。对离散元商业软件进行了二次开发,实现了大小主应力及其应力主方向角的可视化,分析了试样内部的应力偏转情况。同时,以纯转动率和颗粒速度等微观变量为中心,观察了试样内部颗粒的运动状态,解析了直剪试验中砂土剪切带形成的微观机制。研究表明,直剪试验中应变局部化区域集中在剪切面附近的一个条带内。通过转动场和速度场的分析可知,剪切带宽度约为10～15倍的砂土平均粒径,带内颗粒转动明显,带边缘出现大的速度和转动变化梯度。对组构和接触力分布的分析可知,剪切过程中粒间接触点和接触力的主轴方向发生了相一致的偏转,偏转后的主轴方向为60°左右。     

RETRACTED ARTICLE: Numerical analysis of multiphase flow in porous material

Recent developments in the application of x-ray micro-tomography in laboratory geomechanics have allowed all the individual grains of sand in a test sample to be seen and identified uniquely in 3D. Combining such imaging capabilities with experiments carried out “in situ” within an imaging set-up has led to the possibility of directly observing the mechanisms of deformation as they happen. The challenge has thus become extracting pertinent, quantified information from these rich time-lapse 3D images to elucidate the mechanics at play. This paper presents a new approach (ID-Track) for the quantification of individual grain kinematics (displacements and rotations) of large quantities of sand grains (tens of thousands) in a test sample undergoing loading. With ID-Track, grains are tracked between images based on some geometrical feature(s) that allow their unique identification and matching between images. This differs from Digital Image Correlation (DIC), which makes measurements by recognising patterns between images. Since ID-Track does not use the image of a grain for tracking, it is significantly faster than DIC. The technique is detailed in the paper, and is shown to be fast and simple, giving good measurements of displacements, but suffering in the measurement of rotations when compared with Discrete DIC. Subsequently, results are presented from successful applications of ID-track to triaxial tests on two quite different sands: the angular Hostun sand and the rounded Caicos Ooids. This reveals details on the performance of the technique for different grain shapes and insight into the differences in the grain-scale mechanisms occurring in these two sands as they exhibit strain localisation under triaxial loading.     

Role of particle crushing on particle kinematics and shear banding in granular materials

The paper provides an in-depth exploration of the role of particle crushing on particle kinematics and shear banding in sheared granular materials. As a two-dimensional approximation, a crushable granular material may be represented by an assembly of irregularly shaped polygons to include shape diversity of realistic granular materials. Particle assemblies are subjected to biaxial shearing under flexible boundary conditions. With increasing percentage of crushed particles, mesoscale deformation becomes increasingly unstable. Fragmented deformation patterns within the granular assemblies are unable to form stable and distinct shear bands. This is confirmed by the sparsity of large fluctuating velocities in highly crushable assemblies. Without generating distinct shear bands, deformation patterns and failure modes of a highly crushable assembly are similar to those of loose particle assemblies, which are regarded as diffuse deformation. High degrees of spatial association amongst the kinematical quantities confirm the key role that non-affine deformation and particle rotation play in the generation of shear bands. Therefore, particle kinematical quantities can be used to predict the onset and subsequent development of shear zones, which are generally marked by increased particle kinematic activity, such as intense particle rotation and high granular temperature. Our results indicate that shear band thickness increases, and its speed of development slows down, with increasing percentage of crushed particles. As particles crush, spatial force correlation becomes weaker, indicating a more diffuse nature of force transmission across particle contacts.     

Strength of two structured soils in triaxial compression

Oil sands are dense granular materials with interlocked structure and clay shales are heavily overconsolidated clays. They are classified as structured soil or weak rock, exhibiting high peak strength with severe softening and dilation, particularly at low confining stress. The triaxial compression test results indicate that both materials yield linear Mohr–Coulomb envelopes with an apparent cohesion for peak and residual strengths. However, the strength components mobilized from these two materials are very different. This paper investigates if these strength parameters are intrinsic properties or responses derived in triaxial compression conditions. Computer tomography scanning technique is used to aid in examining the micro‐structural features of the sheared specimens such as shear banding pattern, shear band thickness, spatial porosity distributions inside and outside shear bands. These micro‐structural features are used to explain the macro‐deformation response observed in the triaxial compression tests. Mobilization of strength components derived from interlocked structure, cementation, dilation, rolling and critical state are analysed for pre‐, post‐peak softening and residual stages. It is found that the empirical correlation such as Mohr–Coulomb failure criterion based on triaxial compression test results does not necessarily reflect the intrinsic properties of the test materials. Testing conditions are embedded in the empirical correlation. Copyright © 2001 John Wiley & Sons, Ltd.     

Notes on the effect of grain crushing on the granular soil behaviour

Two granular materials — alluvial quartzy Zbraslav sand and granular silica gel — were tested with the intention to demonstrate the effect of grain crushing. Stepwise transformation of the compression curve produced by progressive grain crushing was observed. Due to grain crushing, shear strength envelope became nonlinear, and the behaviour was no more physically isomorphous. The shear stress–strain diagrams acquire a typical wavy (garland-like) form, induced by periodic softening and hardening of the soil response. The intensity of grain crushing depends (in addition to stress level, grain resistance and time) on the shear path. In the crushing phase, initial porosity and angularity play a secondary role. Many other behavioural features common with granular soils (like increase in dilatancy with density and grain size) are suppressed. Grain crushing thus produces a qualitatively different feature of geomaterial behaviour with grave practical consequences (dense sand, e.g. starts to behave like loose).     

Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials

Recent analysis of data from triaxial tests on sand and discrete element simulations indicate the final pattern of failure is encoded in grain motions during the nascent stages of loading. We study vortices that are evident from grain displacements at the start of loading and bear a direct mathematical connection to boundary conditions, uniform continuum strain and shear bands. Motions of three grains in mutual contact, that is, 3‐cycles, manifest vortices. In the initial stages of loading, 3‐cycles initiate a rotation around a region Ω^* where the shear band ultimately develops. This bias sets a course in 3‐cycle evolution, determining where they will more likely collapse. A multiscale spatial analysis of 3‐cycle temporal evolution provides quantitative evidence that the most stable, persistent 3‐cycles degrade preferentially in Ω^*, until essentially depleted when the shear band is fully formed. The transition towards a clustered distribution of persistent 3‐cycles occurs early in the loading history—and coincides with the persistent localisation of vortices in Ω^*. In 3D samples, no evidence of spatial clustering in persistent 3‐cycle deaths is found in samples undergoing diffuse failure, while early clustering manifests in a sample that ultimately failed by strain localisation. This study not only delivered insights into the possible structural origins of vortices in dense granular systems but also a tool for the early detection of the mode of failure—localised versus diffuse—a sample will ultimately undergo. Copyright © 2014 John Wiley & Sons, Ltd.     

A two-scale constitutive framework for modelling localised deformation in saturated dilative hardening material

Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength, which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. It is essential to understand the mechanism behind this internal drainage and to capture it numerically. The purpose of this paper is to develop a macroscopic constitutive relationship for the undrained deformation of saturated dense sand in the presence of a locally fully or partially drained shear band. Separate constitutive relations are generated for the band and intact material. Both time and scale dependence during pore fluid diffusion in saturated sand are captured, eliminating the mesh dependency for finite element implementations. The model is applied to the Gauss points that satisfy the bifurcation criterion. The proposed method is calibrated to recreate the undrained macroscopic response bestowed by an extra-small mesh. The microscopic behaviours inside and outside shear band predicted by this model are qualitatively in good agreement with individual material point behaviours inside and outside the shear band in the extra-small mesh. Depending on the loading rate and the shear band thickness, the response inside the band can be fully or partially drained, which governs the ultimate global strength. The calibrated model is exploited to simulate an upscaled biaxial compression test with semipermeable boundaries.     

Influence of relative density,particle shape,and stress path on the plane strain compression behavior of granular materials

Two types of stress path-controlled plane strain compression tests were performed on both loose and dense specimens of angular and sub-angular sands and two rounded glass beads with different particle sizes. Digital image correlation method was used to analyze local deformation developments, especially shear band patterns. The material behavior in response to shearing has been found to be dependent on the relative density, particle shape, and stress path. The results of analysis on local deformation developments showed that the onset of shear bands occurred prior to their peak strengths in both dense and loose specimens. The growth rates of local maximum shear strain along a shear band were approximately consistent with an increasing global axial strain after the onset of shear band. The shear band width was influenced by both the mean particle size and the particle shape. The measured shear band inclination angles were in between those estimated by Coulomb’s and Roscoe’s formulas.     

Micromechanical investigation of the particle size effect on the shear strength of uncrushable granular materials

Particle size strongly influences the shear strength of granular materials. However, previous studies of the particle size effect have focused mainly on the macroscopic behavior of granular materials, neglecting the associated micro-mechanism. In this study, the effect of particle size on the shear strength of uncrushable granular materials in biaxial testing is investigated using the discrete element method (DEM). First, a comprehensive calibration against experimental results is conducted to obtain the DEM parameters for two types of quartz sand. Then, a series of biaxial tests are simulated on sands with parallel particle size distributions to investigate the effect of particle size on macro- and microscopic behaviors. Finally, by adopting the rolling resistance method and the clump method, irregular-shaped particles are simulated to investigate how the particle size effect will be influenced by the particle shape. Simulation results demonstrate that (1) the peak shear strength increases with particle size, whereas the residual shear strength is independent of particle size; (2) the thickness of the shear band increases with the particle size, but its ratio decreases with particle size; (3) the particle size effect can be explained by the increase of friction utilization ratio with particle size; and (4) the particle size effect is more significant in granular materials that consist of particles with higher angularity.

     

Critical length of force chains and shear band thickness in dense granular materials

This paper investigates the existence of the critical force chain length and the buckling of unconfined grain columns in dense granular materials. Tests on assemblies of flat pentagon photoelastic particles were first carried out to demonstrate the maximum length of force chains. Then, the theoretical buckling analysis and distinct element method (DEM) simulations for grain columns composed of mono-sized elliptical particles were performed. The results revealed the existence of critical column length, which is generally affected by the particle shapes, the rotational resistance at particle contact points and the end constraints to the grain columns. The interparticle friction does not have explicit effect on the critical force chain length, but it has significant influence on the grain column’s curvature when collapse takes place. The thickness of shear band in granular soils can be determined as the critical length of grain columns by appropriately imposing the constraints on the boundaries, as confirmed by DEM simulations and experimental results.     

A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law—expressed solely in terms of particle scale properties—is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.     

From computed tomography to mechanics of granular materials via level set bridge

This paper details the ‘level set bridge’: a single platform for the characterization of various aspects of granular micro-mechanics, including grain morphology, grain kinematics, and inter-granular contact. This platform is studied and verified for accuracy using synthetic examples, in particular, its robustness with respect to the variables of image resolution and noise. The level set bridge is then applied to analysis of XRCT images of real 3D triaxial experiments of two types of granular materials. Contact statistics and kinematics are reported inside and outside of the failure band of one, and kinematics inside a failure band are reported in the other, from preload to critical state.