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.     

高围压下砂土的渗透特性试验研究

利用高压三轴渗透试验系统,对某矿区深部的粗砂和细砂进行了高围压条件下的渗透试验。研究了同一水力梯度下渗透系数与围压的关系;同一围压下渗透系数与渗透水力梯度的关系;同一水力梯度下,围压逐级加载的渗透系数与一次加载的渗透系数之间的差别。结果表明,粗砂和细砂在同一水力梯度下渗透系数均随围压的增大而逐渐减小,在同一围压下,渗透系数会随渗透水力梯度的增大而逐渐增大;同一水力梯度下,围压逐级加载下的渗透系数明显小于一次加载条件下的渗透系数。根据围压与渗透系数的关系拟合出了两种砂样渗透系数与围压关系的数学表达式。为探究高围压下渗透系数变化的原因,研究了砂样试验过程中的体积变化和试验前后的粒度成分变化。结果表明,围压的施加过程伴随着试样的体积减小,相应的孔隙度减小,渗透系数降低;高围压条件下,砂土颗粒被挤碎成细颗粒,使得砂土的细粒含量增多,孔隙度减小,导致了砂土渗透系数的降低。     

砂土有限特征比模型演化规律与参数试验分析

基于有限特征比理论(FCRT),针对构建的FCRT模型,通过试验寻求砂土变形演化规律及模型参数值;该模型理论计算与试验结果对比表明,二者具有很好的一致性,模型客观合理地描述了传统理论模型难以描述的客观现象—不同内部颗粒尺寸、而相同外部尺寸,砂样的不同变形特征,诸如应力等条件一定时,较粗颗粒砂样应变较大。     

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.     

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.     

Experience of Vibrocompaction in Calcareous Sand of UAE

The study is concerned with the influence of various factors on vibro compaction in calcareous soils, This include effect of carbonate content, and influence of pore water pressures in sand, settlements during vibrocompaction, vibroaccelerations during sand column installation compared to earthquake accelerations and finally the liquefaction design based on average CPT parameters. Previous experiences with calcareous sands and literature review confirm the necessity to apply a correlation factor for calcareous material to the raw cone penetration resistance CPT values obtained in the field. Because of the very fragile grains of the Dubai calcareous sands the penetration resistance will be influenced by crushing and grinding. To accommodate for effect of calcareous sands on measured CPT values, a best fit correlations formula called here “correlation factor” is developed. A parametric dynamic triaxial liquefaction testing programme has been executed on representative samples with loose and dense zones. Representative testing parameters for field conditions and earthquake design accelerations have been applied indicating that ground improvement is necessary. It was observed during the dynamic triaxial tests that the whole soil mass consisting of dense columns and looser zones in between behaves jointly, and therefore compaction control using an average-CPT approach is possible.     

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.     

粉细砂的真三轴试验与强度特性

采用柔性真三轴仪对上海粉细砂进行了一系列不同中主应力系数条件下的真三轴试验,针对中主应力对粉细砂强度特性的影响进行了系统分析。基于真三轴试验结果对Mohr-Coulomb强度准则的形状函数进行了改进,并采用试验结果对强度准则进行验证。结果表明,建立在真三轴试验基础上的强度准则能更准确地反映砂土三维应力状态下的强度特性。     

Terminal settling velocity of commonly occurring sand grains

Published measurements of terminal settling velocity for commonly occurring sands are used to develop three equations which join into a single segmented curve of dimensionless form. Results are noticeably different from those for spheres of similar diameter, and permit calculation of the settling velocity for usual sand grains without specification of exact grain shape. For quartz in water, the three equations of different settling regimes correspond approximately to: very fine sand; fine to coarse sand; and very coarse sand.     

Constitutive model for cyclic behaviour of cohesionless sands

This paper presents a constitutive model for describing the stress-strain response of sands under cyclic loading. The model, formulated using the critical state theory within the bounding surface plasticity framework, is an upgraded version of an existing model developed for monotonic behaviour of cohesionless sands. With modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to simulate cyclic loading. The proposed model was validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Nigata sand. Comparison between the measured and predicted results suggests that the proposed modified model can capture the main features of cohesionless sands under drained and undrained cyclic loading.     

Transferable wavelet method for grain‐size distribution from images of sediment surfaces and thin sections,and other natural granular patterns

In images of sedimentary or granular material, or simulations of binary (two‐phase) granular media, in which the individual grains are resolved, the complete size distribution of apparent grain axes is well‐approximated by the global power spectral density function derived using a Morlet wavelet. This approach overcomes many limitations of previous automated methods for estimating the grain‐size distribution from images, all of which rely on either: identification and segmentation of individual grains; calibration and/or relatively large sample sizes. The new method presented here is tested using: (i) various types of simulations of two‐phase media with a size distribution, with and without preferred orientation; (ii) 300 sample images drawn from 46 populations of sands and gravels from around the world, displaying a wide variability in origin (biogenic and mineralogical), size, surface texture and shape; (iii) petrographic thin section samples from nine populations of sedimentary rock; (iv) high‐resolution scans of marine sediment cores; and (v) non‐sedimentary natural granular patterns including sea ice and patterned ground. The grain‐size distribution obtained is equivalent to the distribution of apparent intermediate grain diameters, grid by number style. For images containing sufficient well‐resolved grains, root mean square errors are within tens of percent for percentiles across the entire grain‐size distribution. As such, this method is the first of its type which is completely transferable, unmodified, without calibration, for both consolidated and unconsolidated sediment, isotropic and anisotropic two‐phase media, and even non‐sedimentary granular patterns. The success of the wavelet approach is due, in part, to it quantifying both spectral and spatial information from the sediment image simultaneously, something which no previously developed technique is able to do.     

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter-grains elongation/compression energy from inter-grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model.     

Liquefaction characteristics of silts

Summary The paper presents a summary of the results of cyclical triaxial load testing of samples of silt and silty sands. The paper emphasizes differences in behaviour observed between reconstituted triaxial samples of clean sand, of sand containing 10, 20, 30 and 60% silt, pure silt, and undisturbed samples of silt and silty sand. An important observation is that the mechanisms of deformation for sit are different for reconstituted and undisturbed samples, the undisturbed sample having a specific geological structure which seems to slow down the excess pore water pressure accumulation, but which still results in cyclic deformations regularly increasing from the very beginning of the test and rapidly reaching high levels. The other important observation is that fine-grained noncohesive soils such as silts and silty sands can be as, or even more, susceptible to liquefaction as clean sands. Test results on samples of sand containing 10, 20 or 30% of silt indicate lesser resistance to liquefaction than pure sand samples. The paper shows the difficulty in identifying a representative parameter to compare the behaviour of silts and silty sands with pure sand, and it seems that more research will be needed in this area.     

Concept of critical void ratio used in estimating dynamic stability of sands

Some authors use the concept of critical void ratio of sands to describe sand behavior under dynamic load. This paper presents a new procedure of experimental determination of the critical void ratio of sands under consolidated undrained triaxial compression. At present, there is no technical possibility for determining the critical void ratio of sand under dynamic loads, particularly in shear zones. The mechanism of dynamic load is such that both pore pressure and effective stresses (indirect indicators of the change in the void ratio of sand under undrained conditions) change several times, even during one cycle. It is established that, because of dynamic loading, saturated sands of any density tend to the state of zero dynamic dilatancy when shear zones of constant thickness form in sands, where further strain accumulation is localized. The investigation into the state of zero dynamic dilatancy is fundamentally important for the estimation of the dynamic stability of sands.     

Practical representation of characteristic grain shape of sands: a comparison of methods

ABSTRACT A measure of grain shape is needed for incorporation in calculations of the behaviour of grain populations (for example during transport by fluids). Many shape measures have been proposed, most of them for application to single grains rather than to populations. In this paper three such shape parameters are evaluated for samples taken by size fraction from each of three parent sands. The chosen parameters are the maximum projection sphericity of Sneed & Folk (based on triaxial measurements made on the grains), the dynamic shape factor of Briggs (based on settling velocity in water), and rollability, after Winkelmolen (based on rolling behaviour in a specially mounted rotating cylinder).
It is shown that the Sneed & Folk parameter and rollability both discriminate clearly between the shape characteristics of the three sands over the size range 150-500 μm. Moreover the discrimination of the two parameters is mutually consistent. However, dynamic shape factor gives results which for sizes smaller than 300 μm are inconsistent with those of the other two methods and which do not discriminate reliably between the populations. This is inevitable because the differences between drag on spheres and on other shapes become very small at Reynolds Numbers corresponding to those which obtain in settling tests on grains smaller than 300 μm.     

昌黎海岸风成沙丘砂组构特征及其与海滩砂的比较

对昌黎海岸沙丘砂进行薄片统计,重砂矿物分析,电镜扫描,粒度分析及与海滩砂的对比研究发现,沙丘砂在物质组成、颗粒形态、石英砂表面结构特征和粒度特征方面均继承了海滩砂特征,不过,海滩砂中也有沙丘砂的某些特征,反映了两者沉积的混合。这是由于向岸风和离岸风共同作用的结果。     

剪切作用下钙质砂颗粒破碎试验研究

钙质砂是一种海洋沉积物,与陆源砂比起来,钙质砂受力后易产生颗粒破碎,从而使其力学性质发生变化。对取自南沙群岛永暑礁附近海域的钙质砂进行了不同围压、不同应变下的三轴剪切试验,对试验前后的试样进行了颗粒大小分析试验。试验结果表明,钙质砂在三轴剪切作用下颗粒破碎十分严重,同时用Hardin模型对其破碎进行了度量,并就围压、剪切应变与破碎之间的关系进行了分析。     

三轴试验中砂土刚度的统计和回归分析及应用

砂土的密度和应力状态对其刚度有很大的影响。计算岩土工程中许多硬化土体模型都是基于邓肯−张模型得出的,没有考虑到密度对砂土刚度的影响。而在极致密或松散的砂土的三轴压缩过程中,剪切应变的上升会引起密度的显著变化。为了评估粒径分布、密度及应力状态对砂土刚度的影响,使用统计和回归方法对来自莫斯科和明斯克的15个建筑工地的962个土壤样本的各向同性三轴试验数据进行分析。基于密度和应力状态参数的影响,提出了评估不同粒径砂土刚度的经验方程。对来自欧洲、印度和美国的冲积土和陆地土试验的比较分析表明,其砂土的刚度与莫斯科和明斯克的砂土在同一范围。所提出的方程可用于初步估计有限元法计算里的刚度参数,也可应用于岩土工程模型（允许考虑刚度的变化、水平和垂直分布）。此外,还提出了基于邓肯−张模型的半经验关系。当密度的变化影响土的刚度时,该半经验关系可为受到大变形和（或）复杂加载路径影响的松散和非常致密的砂土提供更为真实的结果。一般来说,岩土工程师可将获得的结果应用于更为复杂的土体模型设计中。     

Significance and origin of surface textures on broken sand grains in deep-sea sediments

The surface textures of fine sand particles from the Deep Sea Drilling Project Leg 39 have been studied via scanning electron microscopy. A large portion of the coarsest fraction of these grains from deep sea cores were formerly fragments of larger sand-sized grains that had been mechanically broken. Surface textures characteristic of previous aeolian and subaqueous environments were preserved in fragments broken from the original larger grain surfaces, thus making palaeo-environmental reconstruction possible. Previously, characteristic mechanical markings had not been observed on deep sea sands; the momentum of grain to grain collisions with respect to fine sands is generally insufficient to initiate mechanical breakage.     

Laboratory determination of mechanical and hydraulic properties of chemically grouted sands

The purpose of this paper is to investigate mechanical and hydraulic properties of sands treated with mineral-based grouts through the results of a laboratory test programme consisting of unconfined compression tests (UCS), triaxial bender element tests (BeT) and constant flow permeability tests in triaxial apparatus. An improved apparatus was set up for obtaining high quality, multiple grouted specimens from a single column. Two selected natural sands having different grain sizes were grouted with two mineral-based silica grouts, resulting in different levels of improvement. The behaviour of the sands treated by mineral grouts, in terms of strength, initial stiffness and permeability, was compared with that exhibited by more traditional silicate grouts. The results of this study indicate that sands treated with mineral grouts result in higher strengths, higher initial shear modulus and lower permeability values than the sands treated with the silicate solution. The effect of grout type, effective confining pressure, and sand particle-size on small-strain shear modulus of grouted sand specimens was evaluated. Based on test results, the small strain shear modulus increment from treated to untreated specimens has been correlated with the unconfined compressive strength, obtaining a unique relationship regardless of grout type and grain-size of tested sands.