A non‐coaxial constitutive model for sand deformation under rotation of principal stress axes

A constitutive model for the simulation of non‐coaxiality, an aspect of anisotropic behavior of sand subjected to the rotation of the principal stress axes, is presented in this paper. Experimental studies have shown that non‐coaxiality or non‐coincidence of principal plastic strain increments with principal stress axes under loadings involving the rotation of principal stress axes may be considerable. Besides, the rotation of the principal stress axes results in dramatic effects on stiffness and dilatant behavior of sand. Therefore, the consequences of principal stress axes rotation on deformational behavior, dilatancy and soil stiffness must be taken into account in theoretical and practical problems. To this aim, the following steps are taken: (1) A general relationship for flow direction with respect to possibility of non‐coaxial flow is developed. Moreover, special circumstances linking non‐coaxiality to instantaneous interaction between loading and soil fabric are proposed. (2) Proposing novel expressions for plastic modulus and dilatancy function, the model is enforced to provide realistic simulations when sand is subjected to the rotation of the principal stress axes. Finally, with numerous examples and comparisons, the model capabilities are shown under various stress paths and drainage conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

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。     

循环荷载下砂土的剪切硬化边界面本构模型

基于临界状态土力学框架,建立了一个适用于往返循环荷载作用的砂土边界面本构模型。采用无纯弹性域假设,认为受到反向荷载的瞬时土体就产生塑性变形,砂土的弹性区域退化为一个点。屈服面为倒子弹头型,由于砂土孔隙比与压力之间不存在惟一对应的关系,使得屈服面大小无法与体积应变直接耦合,故采用塑性偏应变而不是剑桥模型那种塑性体应变作为硬化参数。流动法则采用加入状态参数的修正的Rowe应力剪胀关系,体现了依赖状态的剪胀思想。屈服面大小的比值 反映了塑性模量的演化,并推导了 的表达式。只用1套参数,该模型就能合理地模拟砂土在不同密度和固结压力下循环荷载的应力-应变关系曲线。     

基于临界状态模型的砂土非共轴本构模拟

传统的砂土本构理论隐含了应力和塑性应变率的共轴条件,无法客观描述主应力轴旋转试验中的非共轴现象,并且当密度和围压变化较大时也不适用。基于材料状态相关砂土临界状态概念,将Pietruszczak和Stolle所提出的砂土本构模型进行了改进,并在模型中引入非共轴塑性流动理论来描述非共轴现象。通过对单剪试验和空心圆柱试验进行数值模拟,表明基于临界状态理论的非共轴模型能够合理描述主应力轴旋转过程中砂土的非共轴变形特性     

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.     

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.     

Novel findings on the dilatancy and non-coaxiality of sand under generalised loading

Acta Geotechnica - The dilatancy and non-coaxiality of sand are investigated under generalised loading including rotation of the stress principal axes (PA), in drained and undrained conditions....     

砂土的物态本构模型

基于砂土的压缩回胀性、剪切非线性及剪缩剪胀性的系统分析和包括循环荷载、主应力轴旋转及应力路径偏转等复杂应力条件下的复杂变形反应,得到了三类应力-应变基本关系。在剪缩剪胀应力-应变关系中,引入了由偏应变分量确定的应变路径长度变量,揭示了应力主轴旋转、应力路径偏转引起的剪缩剪胀性。将这些基本关系与循环荷载下砂土的物态变化相联系,建立了砂土的物态动本构关系。     

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.     

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。     

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

Multi-laminate model of clays—a numerical evaluation of the influence of rotation of the principal stress axes

A new framework for the development of constitutive models based on certain aspects of physical theories of plasticity is proposed. The resulting Multi-laminate model of clays has the same response as the Critical state model provided no rotation of principal stress axes takes place during plastic flow. The influence of rotation of the principal stress axes on the volumetric and deviatoric plastic strains has been numerically evaluated. In undrained saturated, normally consolidated clays considerable excess pore pressure may build up due to rotation of the principal axes only. Numerical studies of the collapse of footings indicate that significant rotations do not take place in this class of problems and consequently the collapse load is only marginally reduced.     

偏应力比和应力主轴偏转角同时变化下饱和砂土变形特性研究

利用空心圆柱扭剪仪对饱和砂土进行了应力主轴固定和偏应力比增大（即定向剪切）、偏应力比不变和应力主轴单调旋转（即纯应力主轴单调旋转）、偏应力比和应力主轴偏转角同时增加、偏应力比和应力主轴偏转角分段增加4个系列的排水剪切试验,着重分析不同应力路径下饱和砂土的变形特性及主应力和主应变增量方向变化规律。试验结果表明,纯应力主轴单调旋转下,主应力增量方向在45°～135°范围内变化,主应变增量方向逐渐偏向主应力方向;偏应力比和应力主轴偏转角同时增加下,砂土变形不断增大,当主应力增量方向 45°时,主应变增量方向与主应力增量方向基本一致,但当 45°时,主应变增量方向逐渐偏离主应力增量方向。当应力状态在偏应力比 0.75、应力主轴偏转角 45°范围内时,体应变、最大剪应变与应力路径无关,且后期纯应力主轴旋转下砂土变形不受前期加载历史的影响。     

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。     

Modeling cyclic shearing of sands in the semifluidized state

Liquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress-strain response in earthquake-induced liquefaction and post-liquefaction is complex and yet very important for stress-deformation and performance-based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre-liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post-liquefaction response.     

适用于砂土循环加载分析的边界面塑性模型

基于临界状态土力学框架,建立了一个适用于砂土排水循环加载的边界面塑性模型。采用了考虑虚拟峰值应力比的偏应变硬化准则,初始加载阶段应力点位于边界面上,反向加载阶段以历史最大屈服面作为边界面,同时实现了对密砂软化现象的模拟和对历史所受最大应力的记忆。边界面采用修正的椭圆形,引入考虑密度与应力水平的状态相关剪胀函数,采用非相关联流动法则和以应力反向点作为映射中心的径向映射准则。模型仅有10个参数,通过常规三轴试验即可确定,并且使用一套参数可以模拟不同围压、密度的单调和循环加载情况。分别对饱和砂土的单调、循环排水三轴试验进行模拟,结果表明,该模型能够合理地反映饱和砂土排水条件下的应力-应变特性。     

A two-mechanism soil–structure interface model for three-dimensional cyclic loading

A three-dimensional (3D) soil–structure interface model is proposed within the two-mechanism constitutive theory and bounding surface theory originally established for soils. The proposed model has two main characteristics: first, the model is formulated based on two different and superposed deformation mechanisms. The first mechanism is due to the stress ratio increment, and the second is due to the normal stress increment. Each mechanism induces a shear strain component and a normal strain component. The proposed model can be reduced to the conventional single-mechanism interface model. Second, the plastic modulus and stress dilatancy are defined using the bounding surface theory. The plastic flow rule under cyclic loading is modified and assumed to be dependent on both the stress state of the mapping point and the stress reversal loading direction. The proposed model was validated against the available 3D interface tests and was found to satisfactorily reflect the salient features of the interfaces under monotonic and cyclic loading paths with different normal boundaries. The problem in which the elastic normal stiffness in conventional single-mechanism interface models is often underestimated to enhance the simulation performance under varying normal stress conditions is solved by incorporating the second mechanism. And the effect of the second mechanism on the modeling behavior is discussed. The modified plastic flow direction accurately simulates the 3D cyclic shear response, and the difference between the model simulation and test result increases with the number of cycles by use of the plastic flow direction defined in conventional bounding surface theory.     

高低压下不同力学特性的砂土统一模型

为构建能够反映砂土高低压下不同力学特性的统一模型,分析了砂土在较大的压力范围内的力学试验结果并获取其强度、等向压缩以及临界状态特性参数。通过引入应力路径相关因子来修正塑性应变增量中与应力路径相关的部分,从而使得模型硬化参量能够反映密实砂土在常压下的剪胀特性。同时,基于砂土的临界状态特性提出能够与砂土内部状态相对应的潜在状态面概念,由屈服面与潜在状态面间的动态关系确定加载过程中的动态密实参数及潜在强度,进而使得硬化参量也能够反映密实砂土在常压下的软化特性及高压下的剪缩、硬化特性。分析模型屈服面及潜在状态面间的演化规律并对不同压力等级下的砂土受荷力学行为进行模拟预测,证实了该模型能够反映密实砂土常压下剪胀软化及高压下剪缩硬化的特性。     

堆石料的剪胀特性与广义塑性本构模型

以三轴试验成果为基础,考虑颗粒破碎引起堆石料剪胀比与应力比之间的非线性关系,提出了能够反映堆石料低围压剪胀、高围压剪缩特性的剪胀方程。在广义塑性理论框架内构造堆石料的塑性流动方向向量和加载方向向量,引入依赖于密实度与平均应力的压缩参数,构造随平均应力、剪应力比和密实度变化的塑性模量,建立了一个考虑颗粒破碎的堆石料弹塑性本构模型。阐述了该模型10个参数的确定方法,并通过模拟不同围压和不同应力路径下堆石料的三轴压缩试验资料验证了模型与参数的合理性。