Experimental study of strain localization in sensitive clays

For evaluation of slope stability in materials displaying strain-softening behavior, knowledge concerning the failed state material response is of importance. Here, soft sensitive clay is studied. Such clays behave contractant at failure, which for undrained conditions yields a strain-softening behavior governed by the generation of excess pore water pressure. Strain softening is further linked with material instability and the phenomenon of strain localization. In the case of shear band formation, internal pore pressure gradients are then expected to be present for globally undrained conditions in the sensitive clay due to its low permeability. In the present study, this hypothesis and its implications on the global response and shear band properties are investigated. Utilizing an experimental setup with a modified triaxial cell allowing for shear band formation, the effect of varying the displacement rate is studied. Onset of strain localization is interpreted to occur just before or at the peak shear strength. A strong rate dependency of the softening response is observed. Increasing displacement rates give raised brittleness in terms of the slope of the global softening curve due to accumulating pore pressure. Also, reduced shear band thickness and a shear band inclination approaching 45° are obtained for increasing rates. In the context of slope failure in such materials, the rate dependency in the post-peak state opens up for a large variation in behavior, all depending on time as an important factor.     

Numerically observed shear bands in soft sensitive clays

The numerical challenges that arise in modelling shear bands in soft sensitive (SS) clays have not yet been fully resolved. Convincing and well-accepted solutions have yet to be found. This paper presents some novel information related to the shear band phenomenon in SS clays. In this study, the hypothesis is that the generation and dissipation of excess pore pressure from shear bands could regularise the strain softening and result in a mesh independent shear band thickness. The generation and dissipation of excess pressure is modelled by a coupled consolidation process. The simulation aims at modelling two counteracting mechanisms in the SS clay. First, the shear band narrows because of strain softening. Second, the internal pore water pressure drainage reduces the rate of strain softening. This counteracting mechanism provides an inherent regularisation technique for SS clays. This study presents some numerical results involving these two counteracting mechanisms. This study also shows that an inherent internal parameter applicable for SS clays can be defined by the ratio between soil permeability and the applied strain rate. In the case of SS clays, the range of this parameter varies from 0 to 0.0002 mm.     

Experimental characterization and 3D DEM simulation of bond breakages in artificially cemented sands with different bond strengths when subjected to triaxial shearing

This paper describes the mechanical behavior of artificially cemented sands with strong, intermediate, and weak bond strengths, using experimentation and 3D discrete element method (DEM) simulation. The focus is on the features of bond breakage and the associated influences on the stress–strain responses. Under triaxial shearing, the acoustic emission rate captured in the experiment and the bond breakage rate recorded in the simulations show resemblance to the stress–strain response, especially for strongly and intermediately cemented samples, where a strain softening response is observed. The simulations further reveal the shear band formation coincides with the development of bond breakage locations due to the local weakness caused by the bond breakages. Strain softening and volumetric dilation are observed inside the shear band, while the region outside the shear band undergoes elastic unloading. The weakly cemented sample exhibits a strain hardening response instead; bond breakages and the associated local weaknesses are always randomly formed such that no persistent shear band is observed. Note that in the DEM simulation, the flexible membrane boundary is established by a network of bonded membrane particles; the membrane particle network is further partitioned into finite triangular elements. The associated algorithm can accurately distribute the applied confining pressure onto the membrane particles and determine the sample volume.     

Effect of consolidation on strain localization of soft clays

A finite element formulation developed by Belytschko and his coworkers [1] is used to examine localized deformation as it exists for laboratory specimens of compressible Chicago clays. The element is based on an assumed strain formulation wherein localized and non-localized zones are embedded into an element when material based bifurcation is detected. A plane strain compression test of a natural clay specimen in which deformations localized into a single shear band during undrained shear is simulated using this element. Localization is initiated by imposing a non-uniform applied displacement consistent with that measured experimentally. Results indicate that to insure localization to a single band, considerations must be made for non-uniformities developed during the consolidation phase.     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

砂土的渐进破坏及其数值模拟

紧密砂土在排水剪切过程中由于材料的应变软化特性,会出现变形局部化并伴随剪切带的产生。对此类问题进行数值模拟时会遇到很多困难,比如如何模拟紧砂的应变软化特性,如何处理有限元数值分析过程中刚度矩阵的非正定导致计算结果发散问题,以及如何处理应力不连续的问题,拟针对以上问题进行了探讨。     

不同应力路径下剪切带的数值模拟

采用回映应力更新算法,编写了基于伏斯列夫面的超固结黏土本构关系模型子程序,嵌入非线性有限元软件ABAQUS。通过对单元试验进行三轴压缩、三轴伸长及平面应变等问题的模型预测,再现了超固结黏土在不同初始超固结比和应力路径时的变形和强度特性,从而验证了子程序的正确性。借助该本构模型,对三轴压缩、三轴伸长及平面应变应力路径下超固结黏土体变形局部化问题,进行了三维数值模拟。分析结果表明：超固结黏土在三轴压缩及伸长状态时,土体变形局部化在应力-应变关系软化时出现,而平面应变状态时,在应力-应变关系硬化阶段出现,其超固结黏土的剪胀特性在剪切带的形成过程中起重要作用。     

Numerical modeling of combined effects of upward and downward propagation of shear bands on stability of slopes with sensitive clay

Modeling of progressive development of zones of large inelastic shear deformation (shear band) that results from strain‐softening behavior of sensitive clays could explain the failure mechanisms of large landslides. Because of toe erosion, a shear band can be initiated and propagated upward (inward) from the river bank. On the other hand, upslope surcharge loading could generate shear bands that might propagate down towards the river bank. In the present study, upward and downward propagation of shear bands and failure of sensitive clay slopes are modeled using the Coupled Eulerian Lagrangian approach in Abaqus finite element (FE) software. It is shown that the formation and propagation of shear bands are significantly influenced by kinematic constraints that change with displacements of the soil masses, and therefore the propagation of an existing shear band might be stopped and new shear bands could be formed. The main advantages of the present FE modeling are: (i) extremely large strains in the shear bands can be successfully simulated without numerical issues, (ii) a priori definition of shearing zones is not required to tackle severe strains; instead, the FE program automatically identifies the critical locations for shear band formation and propagation. Toe erosion could significantly increase the slope failure potential because of upslope surcharge loading. FE analyses with a thick and thin sensitive clay layers show that the global failure could occur at lower surcharge loads in the former as compared to the latter cases. Copyright © 2016 John Wiley & Sons, Ltd.     

Monotonic and cyclic modeling of interface between geotextile and gravelly soil

This paper describes a modified elasto‐plasticity damage model to capture monotonic and cyclic behavior of the interface between a geotextile and gravelly soil. New damage variable and shear strength criterion are introduced on the basis of test observations. The formulations of the modified model are obtained by extending those of the original interface model. The model parameters with physical meaning are easily determined from a group of cyclic shear tests and a confining compression test. The model predictions are compared with the results of a series of direct shear tests and large‐scale pullout tests. The comparison results demonstrate that the model accurately describes the monotonic and cyclic stress–strain relationship of the interface between a geotextile and gravelly soil while capturing new characteristics: (1) the strength that is nonlinearly dependent on the normal stress; (2) significant shear strain‐softening; (3) the comprehensive volumetric strain response with dependency on the shear direction; and (4) the evolution of behavior associated with the changes in the physical state that includes the geotextile damage. This model is used in a finite element analysis of pullout tests, indicating that the tensile modulus of a geotextile has a significant effect on the response of the geotextile–gravel system. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Kinematic modelling of shear band localization using discrete finite elements

Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling strain localization in granular materials using micropolar theory: mathematical formulations

It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill‐posedness and mesh dependency. Therefore, a non‐local theory with internal length scales is needed to overcome such problems. The micropolar and high‐order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

基于颗粒抗转动模型的刚性挡墙被动土压力临界状态离散元分析

简要介绍了颗粒抗转动模型,并将其引入离散元程序中,通过建立挡墙地基模型和合理选取模型参数,分别考虑了地基填土不同密实度和挡墙不同位移模式（被动T模式、RB模式、RT模式）情况下,刚性挡墙被动土压力随挡墙位移增长发展到达临界状态时,土压力系数 随位移发展的变化规律及墙后填土剪切带的形成规律,并与其他学者的研究成果进行对比分析。研究结果表明,土压力系数 随着挡墙位移增长的变化规律与填土的孔隙比（或相对密实度）和挡墙的位移模式紧密相关。随着孔隙比的减小或相对密实度的增大,土压力系数 会逐渐由位移硬化特性过渡为位移软化特性。尽管中密试样在双轴压缩试验中呈现出应变软化特性,而中密样的土压力系数 随着挡墙平动位移的增长可能呈现出位移软化特性,也可能呈现位移硬化特性。随着刚性挡墙向墙后土体推移,试样中的剪应变随之增大,并会在墙后形成应变局部化,即剪切带的出现。与室内试验剪应变云图相似,离散元较好地模拟了土压力临界状态时剪切带分布规律。同时,墙后土体表面不再是光滑的平面,而是逐渐隆起的凹凸面;随着挡墙位移增长,土体表面隆起量越来越大,直至土体破坏。     

韧性剪切带形成的岩石流变学特征

本文应用流变学有限元法,建立了韧性剪切带内的温度、应力、应变和位移之间的关系。并对加速蠕变和应变软化两种情况,给出了不同时刻韧性剪切带内的温度、应力、应变、应变率、位移和粘滞系数的分布特征,描述了岩石递进变形的规律。     

韧性剪切带形成的岩石流变学特征

 本文应用流变学有限元法,建立了韧性剪切带内的温度、应力、应变和位移之间的关系。并对加速蠕变和应变软化两种情况,给出了不同时刻韧性剪切带内的温度、应力、应变、应变率、位移和粘滞系数的分布特征,描述了岩石递进变形的规律。     

软土中T型触探仪贯入阻力的数值模拟

T型触探仪近年来在国外的海洋软土地基原位测试中得到了广泛应用,但贯入速率、地基土强度的各向异性与渐进软化等因素对于贯入阻力的影响没有得到系统的研究。在大型有限元软件ABAQUS平台上进行二次开发,针对基于Tresca屈服准则的理想弹塑性模型进行了相应改进,使之可以比较合理地反映上述因素的影响,进而对软土中T型触探仪的贯入机制进行了比较系统的数值分析。计算结果表明,贯入速率、地基土强度的各向异性与强度软化效应对于T型触探仪的贯入阻力系数影响较大。通过与有关极限分析上限解的对比分析,在一定程度上验证了有限元分析结果的合理性。     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

基于梯度塑性本构理论的岩样侧向变形分析(Ⅰ):基本理论及本构参数对侧向变形的影响

研究了岩样在单轴压缩条件下轴向应力．侧向或环向变形的全程曲线特征。基于考虑峰值剪切强度后微小结构之间相互影响和作用的梯度塑性理论，得到了由于剪切局部化而引起的侧向塑性变形。利用虎克定律描述了试件的弹性变形，得到了轴向应力．侧向变形全程曲线的解析解。在软化阶段，试件中部侧向变形及对靠近试件上端或下端部位的侧向变形并不相同。与轴向应力．应变曲线可能出现的回跳现象类似。试件中部轴向应力．侧向应变曲线也可能出现回跳现象。在应变软化阶段，与应力．侧向应变曲线相比，应力．环向应变曲线不容易发生回跳现象。若在试件内部出现多条剪切带，则应该以等效剪切带宽度替代本文中的剪切带宽度。随着剪切带倾角、内部长度参数的降低、剪切模量的增加及弹性模量的降低，轴向应力．侧向应变曲线越陡；甚至能出现弹性回跳。     

Transient bifurcation condition of partially saturated porous media at finite strain

Bifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd.     

Interpretation of the lime column penetration test

Dry soil mix (DSM) columns can be used to reduce the settlement of embankments constructed on soft clays and to improve the stability. During construction the shear strength of the columns needs to be confirmed for compliance with technical assumptions. However, the measurement of the column shear strength can be a contentious issue. All methods of assessing the ultimate shear strength of DSM columns have limitations. These are caused by uncertainties in empirical probe factors required to convert pullout or push in force measured during the lime column penetration test to shear strength and/or testing a small proportion of the DSM column volume and determining whether it is representative of the strength of the entire column. The penetration resistance measured using the lime column test is considered to be more representative of average column shear strength than some other test types. This test can be carried out as a pullout resistance test (PORT) or a push in resistance test (PIRT). Both PORT and PIRT require empirical correlations of measured resistance to an absolute measure of shear strength, in a similar manner to the Piezocone test. In this paper, finite element techniques developed for assessment of T-bar, Ball and Piezocone penetration tests ,  and  are used to assess bounds for the empirical probe factor, N. To simulate the cemented DSM columns, analyses have incorporated a model for a strain softening material. Measured settlements from an embankment constructed on DSM ground improvement are then compared with finite element calculations to infer the shear strength of the columns. These inferred shear strengths are then compared with the results of PORT tests performed beneath the embankment.