宏-细观结合的砂土单剪试验非共轴特性分析

针对传统本构理论无法描述土体单剪试验非共轴变形的不足,采用非共轴修正模型进行改进。模型基于材料状态相关临界状态理论,采用宏-细观结合的方法,将1个新的各向异性状态变量引入本构模型来描述砂土的各向异性。考虑细观组构张量和应力张量的几何关系的变化,模型可以描述砂土在主应力轴旋转条件下材料状态的变化,材料状态变化直接导致模型的硬化规律和剪胀性发生变化,因此,模型可以描述该条件下原生向异性对砂土变形的影响。引入非共轴理论对本构模型进行修正,建立了三维非共轴各向异性模型。单剪试验的加载条件会造成主应力轴相对土体沉积面发生旋转,修正模型不但能够描述砂土在主应力轴旋转条件下其原生各向异性对变形的影响,而且可以描述主应力轴旋转造成的应力诱发各向异性对土体变形的影响,因此,该模型能够对整个单剪试验的变形规律进行描述,而且物理意义清晰。通过铝棒堆积体和Toyoura砂单剪试验验证表明,非共轴修正各向异性模型能对单剪试验的整个变形过程进行较好的模拟。     

等幅剪应变下砂土循环单剪行为的离散元模拟

循环动载下土体变形呈现的复杂各向异性,本质上依赖于土体微观组构特征的演化。为了揭示非比例循环动载下土体变形的微观机制,采用离散元方法模拟砂土的循环单剪行为。应用等幅剪应变的往复加载实现循环单剪应力路径,模拟得到了砂土的循环弱化、剪胀性、非共轴性及微观组构的演化规律。微观模拟表明,在循环剪切过程,土体表现为循环弱化行为,并最终趋于塑性安定状态。而试样组构主方向倾角和组构各向异性系数也会不断增大直至一个稳定值,同时主应变率、主应力轴和组构主方向旋转角度会存在一定的差异,即非共轴现象,随着单调剪切的进行,三者会逐渐趋于一致。土体的剪胀行为表现为循环压密性,而非共轴性呈现逐渐增强的演化规律。循环剪切过程中微观组构的主方向与应力主方向逐渐趋于一致,而微观组构各向异性呈现减弱的演化趋势。     

主应力方向对砂土剪胀性的影响分析

剪胀性是土特有的一种材料属性,而准确地描述砂土的剪胀性则是建立砂土本构模型的重要基础。大量常规三轴试验发现,在以相同加载条件下剪切时密砂和松砂会表现出完全不同的剪胀性和应力-应变关系特性,说明砂土的剪胀性不仅与其所处的应力状态有关,也与其物理状态相关。状态参量理论很好地解释了砂土所处应力状态和物理状态对剪胀性的共同作用。空心扭剪三轴试验仪可以实现不同主应力方向的单调剪切试验。试验结果表明,当砂土以不同主应力方向单调剪切时,即使处于相同初始应力条件和物理状态,砂土也会表现出不同的剪胀性,说明了主应力方向也是决定砂土剪胀性的重要条件。本文通过分析试验中主应力方向对砂土剪胀性的影响,提出了一个含有主应力方向的状态参量,并建立了相应的剪胀方程。通过与试验数据的对比,验证了该方法的正确性和准确性。     

单调荷载下砂土变形过程数值模拟及细观机制研究

采用离散单元法的颗粒流理论,模拟了松砂和密砂在单调荷载作用下的变形过程,研究了砂土渐进破坏过程中的宏观力学行为和细观组构参量的演化规律。采用PFC的FISH语言开发了细观组构统计程序,通过记录加载不同时刻试样的细观参量,如配位数、接触法向分布、粒间法向接触力、切向接触力等的演化,分析了砂土变形过程中细观组构变化与宏观力学响应之间的内在联系。应用表征上述量的组构参数研究了砂土的诱发各向异性,探讨了松砂剪缩、密砂剪胀的细观机制。研究成果对于揭示砂土变形的细观机制以及建立砂土的细观力学模型具有重要意义。     

不同围压下两种沥青混凝土成型试样三轴试验研究

为研究制样方法和围压对沥青混凝土力学特性的影响,进行了沥青混凝土试件的2种制样方法、4组不同围压下静三轴试验。试验结果表明:围压越高,沥青混凝土破坏强度越高,剪胀程度越小。相较于室内模拟钻芯试样,击实成型试样三轴试验应力-应变曲线的峰值强度更高,初始切线模量更大,剪胀现象更加明显;通过邓肯-张模型对试验曲线进行拟合,发现邓肯-张模型对沥青混凝土应力-应变的拟合效果并不好;邓肯-张模型不能模拟沥青混凝土的软化和剪胀现象。     

宏细观结合考虑主应力轴旋转的砂土破坏特性

采用宏细观结合各向异性破坏准则对主应力轴旋转条件下砂土的破坏特性进行分析。该准则是加载应力、组构各向异性程度和应力与组构几何关系3个因素的函数,可描述细观特性对任意应力旋转角度条件下破坏特性的影响。根据空心圆柱扭剪试验的特点推导一般正交坐标系下主应力轴旋转条件下的破坏关系式,考虑应力与砂土细观组构的几何关系,推导的关系式即可分析该条件下破坏特性。材料为各向异性时,主应力轴旋转造成破坏特性发生变化,细观各向异性程度越小变化越小;材料为各向同性时,则不会造成砂土破坏特性的变化。该式表明主应力轴旋转条件下不同破坏特性存在的根本原因是砂土各向异性的存在。采用空心圆柱试验结果进行验证,结果表明建立的关系式能较好描述不同应力加载角度条件下砂土的破坏特性。初步验证了由于砂土各向异性的存在使得主应力轴旋转造成了不同的破坏规律。     

各向异性对软土力学特性影响的离散元模拟

软土预压工程中,初始和诱发各向异性对软土力学性质的影响十分显著,而现有研究缺乏对初始和诱发各向异性的统一研究方法。采用离散单元法,以颗粒长宽比作为定量评价指标,构建真实形态的颗粒模型,生成5组不同沉积角的初始各向异性试样,并进行竖直和水平两方向加载的双轴模拟实验,研究了初始各向异性和诱发各向异性对软土力学特性影响;在细观层面,以颗粒为对象研究了颗粒接触形式和转动角度的变化规律,以接触为对象研究了配位数和接触法向各向异性的发展趋势,在此基础上探究抗剪强度指标与各向异性关系。结果表明:初始和诱发各向异性共同影响试样力学性质,当加载方向和软土沉积方向垂直时,土体有最大的峰值强度。颗粒接触形式中面面接触的比例随加载的进行逐渐增大,并影响着试样初始模量和抗剪强度,配位数和接触法向各向异性受颗粒接触形式的影响有不同的演化规律,并在加载后期趋于稳定;同时,初始各向异性试样相较各向同性试样有更大的黏聚力,诱发各向异性主要影响试样内摩擦角,进而影响试样抗剪强度。     

考虑组构变化效应的饱和密砂循环本构模型

为了真实地描述饱和密砂在循环加载过程中的变形行为,需要引入考虑剪胀阶段组构变化的宏观参量。在已有的基于状态参量的本构模型基础上,引入反映组构变化的剪胀内变量,简称组构-剪胀内变量z。以相变线PTL作为参考线,采用基于相变的状态参量判断砂土在初始时刻和任意时刻体积变形的变化趋势,并通过z对剪胀比d的影响,考虑反向加载过程中塑性变形的累积,建立了一个针对饱和密砂的循环加载的弹塑性本构模型。该模型根据试验现象将已有模型中的塑性剪切模量区分为首次加载模量与再加载模量,能较好地模拟排水情况下砂土循环加载的胀-缩变化过程。最后,针对密砂的三轴排水情况,利用文中模型进行预测,并把预测结果与试验结果进行比较,结果表明该模型能够总体反映砂土循环加载的变形行为。     

基于修正应力法的横观各向同性摩尔-库仑准则及被动土压力公式

采用修正应力法考虑各向异性对土的抗剪强度的影响,该方法引入组构张量调整不同方向应力分量的相对大小,使得各向异性土在修正应力空间中等效成各向同性土。用修正应力张量代替真实应力张量,就能将摩尔-库仑强度准则发展至横观各向同性,公式的形式不发生改变,强度参数仍为与加载方向无关的常量。通过对比根据3种不同的修正应力公式得到的内摩擦角与加载方向的关系曲线,分析了组构值对内摩擦角变化规律的影响,在偏平面上绘出了连续规则的强度包线,并预测了不同各向异性岩土类材料的三轴压缩和真三轴试验结果。最后,根据横观各向同性摩尔-库仑准则计算水平沉积地层中挡土墙上的被动土压力,得到了简洁的显式表达式,验证了修正应力法的实用性。     

人工胶结砂土力学特性的离散元模拟

采用离散单元法（DEM）对胶结砂土力学特性进行模拟。将基于室内试验测得的理想胶结颗粒接触力学响应引入到开发的二维离散元程序（NS2D）中,模拟胶结砂土颗粒间的胶结作用。对不同胶结强度和围压的胶结砂土进行平面应变双轴压缩试验模拟,并将模拟结果与Wang和Leung[1]提供的人工胶结砂土的试验结果进行比较。最后对数值模拟中胶结试样的微观力学响应（接触力链、胶结点破坏率和位移场）进行分析。结果表明,离散元数值模拟能够有效地反映胶结砂土的主要力学特性,相比同一初始孔隙比的无胶结松散砂土,胶结砂土将具有更高的强度,应力-应变关系呈应变软化,体变为先剪缩后剪胀,且两者的差异随胶结强度的增大和围压的减小而越趋显著。此外,胶结砂土宏观力学响应（应力-应变关系和剪胀性）与其微观力学响应密切相关。     

A hypoplastic model for granular soils incorporating anisotropic critical state theory

It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress-strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus-Bauer hypoplastic model, and a scalar-valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis

This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two‐dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles. Copyright © 2003 John Wiley & Sons, Ltd.     

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second-order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a₁ and a₂ , control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a₂ as well as the first mode by the parameter a₁ . The third parameter, θ₀ , expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal-stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.     

Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils

In order to simulate the soil response during principal stress rotation, anisotropic unified hardening (UH) model is developed within the framework of elastoplastic theory. Without introducing any additional mechanism to display the role of stress rotation specifically, this model achieves the simulation by considering the material anisotropy. The effect of inherent anisotropy is reflected using the anisotropic transformed stress method, but a new formula for the stress mapping is adopted to keep the mean stress unchanged. Analysis indicates that from the view of the transformed stress tensor, the anisotropic soil is subjected to loading during pure rotation of principal stress axes, so that plastic strains can be calculated. To represent the induced anisotropy, a fabric evolution law is proposed based on laboratory and numerical test results. At the critical state, the fabric tensor reaches a stable value determined by the stress state, while the critical state line is unique in the plane of void ratio versus mean stress. The anisotropic UH model has concise formulation and explicit elastoplastic flexibility matrix and can provide reasonable predictions for the deformation of anisotropic soils when principal stresses rotate.     

A micromechanics-based model for estimating localized failure with effects of fabric anisotropy

This paper presents a micromechanics-based approach to investigate the effects of fabric anisotropy on the behavior of localized failure in granular materials. Based on a micromechanical analysis, the origin of deviatoric stress is decomposed into two components: contact force anisotropy and fabric anisotropy. Using a micro–macro approach, the back stress is interpreted as an contribution to the change of the fabric’s principal direction. The evolution of the back stress is deduced from the stress–fabric relationship and determined with reference to the deviation of the principal directions between the rate of the reduced stress tensor and the actual reduced stress tensor. With this micro–macro framework, a mixed (isotropic–kinematic) hardening model is developed based on the classical isotropic hardening theory. A laboratory simple shear test is first analyzed to validate the proposed model and illustrate the kinematic-hardening mechanism which is usually displayed under non-proportional loading. The analysis further focuses on the anisotropic aspect of localized failure. It has been discovered that the fabric anisotropy can play an important role in the occurrence of shear banding. An increasing degree of fabric anisotropy tends to delay the initiation of the strain localization and result in higher failure strength. The effects of fabric anisotropy have also been illustrated by comparing the theoretical predictions and measured results on the shear band inclination angle, shear strain level and dilatancy at bifurcation.     

A critical state sand plasticity model accounting for fabric evolution

Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

The signature of shear-induced anisotropy in granular media

This paper presents a micro-mechanical study on the characteristics of shear-induced anisotropy in granular media. Based on three-dimensional Discrete Element Method (DEM) simulations, the distinct features associated with the evolution of internal granular structure and different anisotropy sources during drained/undrained shearing of granular samples are carefully examined. The study finds that static liquefaction occurs when the geometrical anisotropy in a sample dominates the mechanical anisotropy in the overall shear strength, and the weak force network features an exceptionally high proportion of sliding contacts and develops certain degree of anisotropy. Phase transformation corresponds to a transitional, unstable state associated with a dramatic change in both coordination number and the proportion of sliding contacts in all contacts. The critical state in a granular material is always associated with a highly anisotropic fabric structure wherein both the critical void ratio and critical fabric anisotropy are uniquely related to the mean effective stress. The relations provide a more comprehensive definition for the critical state in granular media with proper reference to the critical fabric anisotropy.     

Strength anisotropy of granular material consisting of perfectly round particles

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.