Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 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.     

Strain localization in soft rock—a typical rate‐dependent solid: experimental and numerical studies

Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Inelastic constitutive properties and shear localization in Tennessee marble

The inelastic response of Tennessee marble is modelled by an elastic plastic constitutive relation that includes pressure dependence of yield, strain‐softening and inelastic volume strain (dilatancy). Data from 12 axisymmetric compression tests at confining pressures from 0 to 100 MPa are used to determine the dependence of the yield function and plastic potential, which are different, on the first and second stress invariants and the accumulated inelastic shear strain. Because the data requires that the strain at peak stress depends on the mean stress, the locus of peak stresses is neither a yield surface nor a failure envelope, as is often assumed. Based on the constitutive model and Rudnicki and Rice criterion, localization is not predicted to occur in axisymmetric compression although faulting is observed in the tests. The discrepancy is likely due to the overly stiff response of a smooth yield surface model to abrupt changes in the pattern of straining. The constitutive model determined from the axisymmetric compression data describes well the variation of the in‐plane stress observed in a plane strain experiment. The out‐of‐plane stress is not modelled well, apparently because the inelastic normal strain in this direction is overpredicted. In plane strain, localization is predicted to occur close to peak stress, in good agreement with the experiment. Observation of localization on the rising portion of the stress–strain curve in plane strain does not, however, indicate prepeak localization. Because of the rapid increase of mean stress in plane strain, the stress–strain curve can be rising while the shear stress versus shear strain curve at constant mean stress is falling (negative hardening modulus). Copyright © 2001 John Wiley & Sons, Ltd.     

液化后砂土流体特性测试装置的研发及试验研究

为研究液化砂土的流动变形特征,开展了液化砂土的流体特性试验研究。基于边界层理论研发一套液化砂土表观黏度测试装置,主要由调速电机、电机调速器、圆柱转子、扭矩传感器等部分组成,该装置能有效测试液化砂土的表观黏度;开展了不同孔压比、转速下饱和砂土表观黏度及圆柱转子所受摩擦力矩特性研究,着重分析了液化后砂土的表观黏度特性。结果表明,液化前孔压发展及液化后孔压消散阶段摩擦力矩均受到孔压比及转速的影响;液化后砂土孔压逐渐消散,强度恢复,流动能力衰减,表观黏度升高,表观黏度与孔压比呈现出一定的线性相关性;表观黏度随着剪应变率的增大而降低,且两者呈现出幂函数关系,表明液化后砂土具有典型幂律型剪切稀化非牛顿流体特征。     

Strain localization in clay: plane strain versus triaxial loading conditions

The paper presents a comparison between the behavior of slurry-consolidated Kaolin specimens tested under axisymmetric Conventional Triaxial Compression (CTC) and Plane Strain (PS) loading conditions. The PS experiments were conducted on an instrumented apparatus capable of capturing the onset of shear bands. The specimens were consolidated and then sheared under undrained condition. The PS specimens failed via a well-defined shear band that began to develop during the hardening stress regime whereas CTC specimens failed through a diffuse bulging mode. The undrained shear strength (S _u) of CTC experiments is smaller than the S _u of PS experiments. However, the normalized S _u of CTC experiments is very close to PS1, which was consolidated under similar K _o condition.     

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。     

Undrained behaviour of Changi sand in triaxial and plane-strain compression

The results of an experimental study of the undrained behaviour of Changi sand under axisymmetric and plane-strain conditions are presented. K₀ consolidated undrained plane-strain tests and K₀ or isotropically consolidated triaxial tests on very loose and medium dense specimens were conducted. The undrained behaviour of sand at very loose and medium dense states under plane-strain conditions was characterised and compared with that under axisymmetric conditions. It was observed that the undrained behaviour of very loose and medium dense sand under plane strain is similar to that under axisymmetric conditions. However, because of the formation of shear bands in plane-strain tests, the post-peak behaviour of medium dense sand in plane strain is different from that in triaxial tests. It was also established that an instability line for plane-strain conditions can be defined in a way similar to that for axisymmetric conditions. Using the state parameter, a unified relationship between the normalised slope of instability line and the state parameters can be established for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can be used for plane-strain conditions.     

The interaction between reaction and deformation: an experimental study using a biotite + plagioclase + quartz gneiss

Metamorphic reactions commonly accompany ductile deformation of crustal rocks. We performed an experimental study to determine: (i) the effect of syn-deformation reaction on strain weakening and localization, and (ii) the effect of crystal plastic deformation on reaction extent and distribution. Experiments were conducted on a fine-grained gneiss (58 vol.% quartz, forming the interconnected matrix, 13 vol.% biotite, 28 vol.% plagioclase and 1 vol.% garnet/Fe-Ti oxides). General shear experiments were performed at 745 and 800 °C, 1.5 GPa, two strain rates, and shear strain ( γ ) from 0.6 to 5, yielding three suites with initial phase strength contrast between the matrix quartz and weak biotite of 45×, 25× and 10×; hydrostatic experiments were performed on cores and powders at 750 and 800 °C and 1.5–2 GPa for the same times. At these conditions, biotite reacts with plagioclase and quartz to form garnet, K-feldspar and water (no melt was observed). Greater reaction extent was observed in deformed samples than in equivalent hydrostatic samples, because of the increased surface area and internal strain energy. In all of the deformed samples, reaction contributes to strain weakening, due principally to a switch to grain boundary sliding in the fine-grained reaction products. The degree to which syn-deformational reaction causes strain weakening and localization in this polyphase aggregate depends on the phase strength contrast and how it evolves. In samples with low-phase strength contrast, strain and reaction are homogeneously distributed; however, in samples with high-phase strength contrast, ductile strain and reaction interact positively to produce a narrow ductile shear zone. Similar concentration of reaction is observed in some natural ductile shear zones.     

土工环剪仪的开发及其应用研究现状

在回顾国内外有关土工环剪仪研发及其应用研究工作的基础上,介绍了环剪试验设备的开发历程以及当今国际上对环剪试验系统研制方面的最新进展。总结了环剪仪在土工研究工作中的应用情况以及新的试验方法和测试技术等。着重阐述了利用环剪试验在对土峰后应变软化现象与残余强度分析、土的剪切带形成机制试验研究、地质灾害成因机制分析以及土工合成材料界面抗剪强度测定等方面研究中的主要内容、方法和成果。     

Strain localization due to structural in-homogeneities in the Central European Basin System

The large-scale crustal deformations observed in the Central European Basin System (CEBS) are the result of the interplay between several controlling factors, among which lateral rheological heterogeneities play a key role. We present a finite-element integral thin sheet model of stress and strain distribution within the CEBS. Unlike many previous models, this study is based on thermo-mechanical data to quantify the impact of lateral contrasts on the tectonic deformation. Elasto-plastic material behaviour is used for both the mantle and the crust, and the effects of the sedimentary fill are also investigated. The consistency of model results is ensured through comparisons with observed data. The results resemble the present-day dynamics and kinematics when: (1) a weak granite-like lower crust below the Elbe Fault System is modelled in contrast to a stronger lower crust in the area extending north of the Elbe Line throughout the Baltic region; and (2) a transition domain in the upper mantle is considered between the shallow mantle of the Variscan domain and the deep mantle beneath the East European Craton (EEC), extending from the Elbe Line in the south till the Tornquist Zone. The strain localizations observed along these structural contrasts strongly enhance the dominant role played by large structural domains in stiffening the propagation of tectonic deformation and in controlling the basin formation and the evolution in the CEBS.     

Interactions between serpentinite devolatilization, metasomatism and strike-slip strain localization during deep-crustal shearing in the Eastern Alps

The Greiner shear zone in the Tauern Window, Eastern Alps, changes from a zone of distributed (dominantly sinistral) shear in supracrustal rocks to a series of narrow, gully forming dextral splays where it enters basement gneisses. Within these splays, granodiorite is transformed into quartz‐poor biotite and/or chlorite schists, reflecting hydration, removal of Si, Ca and Na, and concentration of Fe, Mg and Al. Stable isotope analyses show a prominent increase in δD and a decrease in δ¹⁸O from granodiorite into the shear zones. These changes indicate significant channelized flow of an externally derived, low‐δ¹⁸O, high‐δD fluid through the shear zones. The shear zone schists are chemically similar to blackwall zones developed around serpentinite bodies elsewhere in the Greiner zone and the stable isotope data support alteration via serpentinite‐derived fluid. Monazite in schist from one shear zone yields spot dates of 29–20 Ma, indicating that the fluid influx and switch from sinistral to dextral shear occurred at or shortly after the thermal peak of the Alpine orogeny (c. 30 Ma). We suggest that Alpine metamorphism of serpentinites released large amounts of high‐δD, low‐δ¹⁸O, Si‐undersaturated, Fe + Mg‐saturated fluids that became channelized along prior zones of weakness in the granodiorite. Infiltration of this fluid facilitated growth of chlorite and biotite, which in turn localized later dextral strain in the narrow splays via cleavage‐parallel slip. This dextral strain event can be linked to other structures that accommodated tectonic escape of major crustal blocks during dextral transpression in the Eastern Alps. This study shows that serpentinite devolatilization can play an important role in modifying both the chemistry and rheology of surrounding rocks during orogenesis.     

平面应变状态下岩石剪切带网络数值模拟研究

研究了围压、端面约束、试件高度及界面特性对剪切带网络形成的影响。首先对影响剪切带网络形成的因素（包括试件高度、围压及温度、试件端部轴向应变大小的计算方法的差异）进行了分析。之后采用FLAC 3D对平面剪切带网络进行了数值模拟,其中摩擦角及内聚力为应变软化。探讨了倾向于出现剪切带网络的若干条件。若端面缚束较强且存在一定的侧压力,试件中部出现多重剪切带。若端面缚束较弱,试件端部易于形成剪切带网络,且随试件高度的增加剪切带条数增加。界面法向和切向刚度越大,剪切带穿越断层并按其固有方向延伸能力越强,剪切带网络格局越明显。获得的数值结果可在实验中找到佐证,并且可以用来解释地震中的一些剪切应变局部化现象。     

材料状态对干砂小应变特性的影响

利用注能虚拟质量(EIVM)共振柱系统进行了干砂小应变特性试验,研究了有效平均正应力、土样密度、剪应变幅值以及荷载往复次数对剪切模量和阻尼比的影响。试验结果表明,剪切模量随有效平均正应力与土样密度的增加而增加,而阻尼比的变化规律则与之相反,并且有效平均正应力对干砂小应变特性的影响程度比土样密度的影响程度大得多;随着剪应变的增加,剪切模量越来越小,而阻尼比越来越大;荷载往复次数对剪切模量基本没有影响,而对阻尼比有较大影响。     

An experimental investigation of LNAPL migration in an unsaturated/saturated sand

Accidental spills of hydrocarbons, such as Light Non-Aqueous Phase Liquids (LNAPLs), are one of the most common sources of subsurface contamination. Migration of LNAPL in a porous medium is influenced by various factors such as the number of fluids present in the unsaturated/saturated zones and the proportion of pores occupied by each fluid. The results for relationship between matric suction and degree of saturation are presented in this paper for water–air, water–LNAPL and LNAPL–air systems in a sand. A simple and reliable setup using Buchner funnel was designed to obtain these relations. It was found that the relationship between matric suction head and degree of saturation is hysteretic for all the fluid systems (water–air, water–LNAPL and LNAPL–air). Furthermore, the amount of hysteresis depended upon the fluid system, with the maximum hysteresis occurring for water–air system. The results suggest that the amount of trapped air depends upon the reversal degree of saturation from drying to wetting.     

Thermo-hydro-mechanical modeling of unsaturated soils using isogeometric analysis: Model development and application to strain localization simulation

This study presents a thermo-hydro-mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA-FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker-Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi-static loading conditions. Temperature dependency of the surface tension is implemented in the soil-water retention curve. Nonuniform rational B-splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA-based framework offers a viable alternative for solving THM problems in unsaturated soils.     

用线状被动标志物向分布估测岩石总体应变的最优化方法

在一些假设下提出了利用线状被动标志物的方向数据估测岩石总体应变的最优化方法。该方法等同地考虑到每个测量数据对应变估计的贡献,从而能够较好地反映出岩石的总体应变。它具有较好的稳健和广泛的适用对象。实验表明,观察数据大约在80个或更少时估测的应变椭圆轴比的相对误差小于20％,超过160个观察数据一般小于5％－10％。     

The solution of the double-sphere model and experimental research of the longterm shear strength of frozen sand based on spherical template indenter test北大核心CSCD

The distribution of frozen soil in our country is very broad, and the area of permafrost alone accounts for 22. 4% of the total land area. As a special kind of soil, frozen soil has many properties that thawing soil does not have due to the influence of ice cement in the soil. Among the many properties of frozen soil, the deformation and strength of frozen soil are the basic problems affecting engineering construction in frozen soil areas. The spherical template indenter test is widely used in the test of the mechanical properties of frozen soil because of its simple test process and relatively accurate test results. Compared with the conventional triaxial test or direct shear test, the test process of the spherical template indenter test is simple and easy to implement, the test period is short, and the sample preparation requirements are low. The advantage of effective cohesion is more significant. Therefore, based on the spherical template indenter test of the frozen soil, this paper estimates the strength and mechanical index of the soil through the indentation depth of the spherical template indenter test, and establishes the relationship between the force of the sample and the indentation depth of the indenter test. The specific test method is as follows:take the water-saturated frozen sandy soil made of different particle size groups(the moisture content of the sample is affected by the particle size in the saturated state)as the research object, study the variation law of the depth of the frozen soil sample pressed into the soil by the spherical indenter with time under the conditions of different fixed loads. By comparing and referring to the frozen sands of each particle size group, the long-term equivalent cohesion of the frozen sands of different particle size groups is summarized. The change law of force(long-term shear strength)with time, and the research method of elastic mechanics to solve space problems, summed up the mutual conversion between the depth St of spherical template indenters pressed into frozen sand samples under different fixed load test conditions relation. The research results show that the long-term shear strength of frozen sand based on the spherical mold test is positively correlated with its particle size. At the same time, since the ice content of frozen soil samples is proportional to its particle size, the long-term shear strength of frozen sand is also proportional to the test. The ice content of the sample increases year-on-year;the long-term shear strength of the frozen sand is related to the maximum contact pressure on the contact surface between the frozen soil and the indenter during the test, which can be expressed as Ct = γq0. The size of the relationship coefficient γ is inversely proportional to the diameter of the spherical indenter. In this paper, the spherical indenter is selected as 22 mm, and γ=3. 82×10-3. By establishing the relationship between the maximum contact pressure q0 and the long-term shear strength Ct When the maximum contact pressure q0 is the same under different fixed loads, the long-term shear strength Ct is also the same. According to this, the depth curve and the freezing depth of the frozen sand pressed into the soil by the spherical indenter over time under different fixed loads can be converted. Long-term shear strength curve of frozen sandy soil with time. It has been verified by experiments that the conversion curve of the depth of the indenter pressed into the soil with time under a fixed load of 7. 0 kg is highly consistent with the measured curve of the depth of the indenter pressed into the soil with time under a fixed load of 5. 1 kg and 7. 0 kg. © 2022 Nanjing Forestry University. All rights reserved.     

Effect of grain crushing on shear localization in granular bodies during plane strain compression

This article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations. Copyright © 2011 John Wiley & Sons, Ltd.