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。     

考虑渐近状态特性的超固结土本构模型

基于超固结土的UH模型,结合渐近状态概念,将适用于饱和砂土的渐近状态本构模型推广为考虑渐近状态特性的超固结土本构模型,用于描述土的超固结性和渐近状态特性。通过采用变换应力方法实现了模型的三维化。新提出的本构模型简单、参数较少,与剑桥模型相比,仅增加了一个材料参数,即伏斯列夫面斜率。该模型能够合理反映超固结土的硬化、软化、临界状态、剪缩、剪胀、应力路径依赖性、渐近状态等特性。     

Development in modeling cyclic loading of sands based on kinematic hardening

In this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou‐Jafari‐Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non‐associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress–dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniqueness and existence in plasticity models for unsaturated soils

The paper investigates the mathematical structure of plasticity models for unsaturated soils and provides a strategy to capture the loss of uniqueness of the incremental solution upon loading and/or wetting paths. To derive bifurcation conditions in simple analytical form, the analysis is restricted to isotropic stress states. This choice has allowed the inspection of the most common classes of constitutive models through a unified notation, as well as the study of different forms of coupling between plasticity and state of saturation. It is shown that, similar to saturated soil plasticity, the loss of admissibility of the plastic solution is governed by critical values of the hardening modulus. At variance with the classical case, however, these moduli can be positive even if the plastic flow rule is associated (bifurcation in the hardening regime). The paper shows that such non-trivial features derive from hydro-mechanical coupling, i.e. they depend on the approach used to reproduce suction effects and evolving retention properties. In other words, although the problem of loss of uniqueness affects all classes of plasticity models for unsaturated soils, different constitutive assumptions may not have the same outcome in terms of bifurcation potential. As a result, new concepts are introduced to compare the mathematical robustness of the different constitutive approaches, as well as to interpret their predictions in the light of precise bifurcation criteria.     

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。     

冻融循环作用下泥质白云岩力学特性及损伤演化规律研究

针对饱水状态下的泥质白云岩,采用BCD–218 C低温数控恒温箱、WDW3100型微机控制电子万能试验机进行不同冻融循环状态下的单轴压缩试验,对其在单轴状态下应力-应变曲线变化特征以及抗压强度、峰值应变、弹性模量、泊松比的变化规律进行了分析。在现有的损伤力学理论基础上,引入斜率增大趋势系数,建立了以冻融循环次数和应变为控制变量的本构模型。结果表明,在冻融循环过程中,单轴抗压强度、峰值应变、弹性模量参数呈指数下降趋势,泊松比呈线性增加的趋势;受冻融循环的影响,应力-应变全过程曲线在第一阶段后出现短暂的线形平缓阶段,具有岩石局部滑移现象;岩石破坏形态从脆性向延性转化,具有峰前塑性硬化和峰后应变软化等行为特征。理论本构模型与试验结果相符合。     

SANISAND-FN: An evolving fabric-based sand model accounting for stress principal axes rotation

SANISAND is the name of a family of bounding surface plasticity constitutive models for sand within the framework of critical state theory, which have been able to realistically simulate the sand behavior under conventional monotonic and cyclic loading paths. In order to incorporate the important role of evolving fabric anisotropy, one such model was modified within the framework of the new anisotropic critical state theory and named SANISAND-F model. Yet the response under continuous stress principal axes rotation requires further modification to account for the effect of ensuing noncoaxiality on the dilatancy and plastic modulus. This modification is simpler than what is often proposed in the literature, since it does not incorporate an additional plastic loading mechanism and/or multiple dilatancy and plastic modulus expressions. The new model named SANISAND-FN is presented herein and is validated against published data for loading that includes drained stress principal axes rotation on Toyoura sand.     

Stress–dilatancy based modelling of granular materials and extensions to soils with crushable grains

Stress–dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics. In this paper, a method to construct thermodynamically consistent (isotropic, three‐invariant) elasto‐plastic models based on a given stress–dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

一类新型的散粒型土体本构理论

详细地介绍了国际上近30才发展起来的具有独特建模思想的一类新型的散粒型土体本构建模理论--亚塑性本构理论。将该理论与经典的弹塑性理论进行比较后发现,亚塑性理论的本构表达式自动隐含了弹塑性理论中相对应的一些基本概念和假定,无需额外引入,因此增加了模型的客观性。以Gudehus-Bauer亚塑性模型为例,分析了模型在临界状态时的本构特征。此外,通过三轴试验和循环剪切试验的亚塑性数值模拟表明,亚塑性本构模型能很好地反映无黏性散粒型土体的非弹性、非线性及剪胀（剪缩）性等主要应力-应变特性。     

Prediction of flow liquefaction instability of clean and silty sands

Adding a small amount of non-plastic silt to clean sands may lead to dramatic loss of shear strength and a noteworthy tendency toward contraction when the mechanical behavior of the mixture is compared with that of the clean host sand. Thus, simulation of the behavior of silty sands with varying fines content is still a challenging subject in geomechanics. A unified constitutive model for clean and silty sands is presented in this paper. To eliminate the factitious decrease of void ratio associated with inactive silt particles in various silty sand mixtures, the concept of equivalent void ratio is used in the model formulation instead of the global void ratio. In addition, the instantaneous soil state is expressed in terms of intergranular state parameter taking into account the combined influence of intergranular void ratio, mean principal effective stress and fines content. Then, dilatancy and plastic hardening modulus are directly linked to the intergranular state parameter. To improve the model capacity in simulation of cyclic tests, new features are added to the plastic hardening modulus. It is shown that the proposed model can reasonably reproduce the mechanical behavior as well as the onset of flow liquefaction instability of clean and silty sands using a unique set of parameters.     

A bounding surface model for saturated and unsaturated soil-structure interfaces

In many geotechnical systems, such as reinforced slopes and embankments, soil-structure interfaces are often unsaturated. Shear behaviour of unsaturated interfaces is strongly dependent on their matric suctions, as revealed by the results of extensive laboratory tests. So far, constitutive models for unsaturated interfaces are very limited in the literature. This paper reports a new bounding surface model for saturated and unsaturated interfaces. New formulations were developed to incorporate suction effects on the flow rule and plastic modulus. To examine the capability of the proposed model, it was applied to simulate suction- and stress-controlled direct shear tests on unsaturated soil–cement, soil–steel and soil–geotextile interfaces. Measured and computed results are well matched, demonstrating that the proposed model can well capture key features of the shear behaviour of unsaturated interfaces, including suction-dependent dilatancy, stress–strain relation and peak and critical state shear strengths.     

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。     

不同加载方向条件下堆石料剪胀特性试验研究

剪胀方程描述的是塑性应变增量比例大小的变化规律,是构建弹塑性模型的重要组成部分。然而目前堆石料的剪胀方程大都是根据等围压 路径得到的,这些剪胀方程是否能反映不同应力路径条件下堆石料的剪胀规律还尚不明了。开展了等围压 、等轴向力 、等平均主应力p、等主应力比 共4种应力路径下的堆石料大型三轴试验,研究了应力路径对堆石料剪胀规律的影响。试验表明：不同路径的剪胀比 和应力比 均呈近似线性关系,但剪胀比与应力比不存在一致的关系,表现出明显的应力路径相关性;在 - 空间中,剪胀线随着应力增量方向的变化会发生平移和转动,其斜率 和截距参数 均随 ( )的增大而增大;目前的剪胀理论不能较好地描述剪胀的应力路径相关性,提出了一个考虑应力增量方向影响的修正剪胀方程并对其进行了试验验证。     

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.     

Modeling the effect of wetting on the mechanical behavior of crushable granular materials

It is well known that the compressibility of crushable granular materials increases with the moisture content,due to the decrease of particle strength in a humid environment.An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work.But how the material humidity can affect this relationship is not clear,and experimental evidence is quite scarce.Based on compression tests on dry and saturated crushable sand recently reported by the present authors,a new non-linear relationship is proposed between the amount of particle breakage and the plastic work.The expression contains two parameters:(1)a material constant dependent on the grain characteristics and(2)a constant depending on the wetting condition(in this study,dry or saturated).A key finding is that the relationship does not depend on the stress path and,for a given wetting condition,only one set of parameters is necessary to reproduce the results of isotropic,oedometric,and triaxial compression tests.The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression.The breakage ratio is introduced into the expression of the elastic stiffness,the critical state line and the hardening compression pressure.Incremental stress-strain computations with the model allow the plastic work to be calculated and,therefore,the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations.Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained.     

Effective stress concept in unsaturated soils: Clarification and validation of a unified framework

The effective stress principle, conventionally applied in saturated soils, is reviewed for constitutive modelling purposes. The assumptions for the applicability of Terzaghi's single effective stress are recalled and its advantages are inventoried. The possible stress frameworks applicable to unsaturated soil modelling are reassessed in a comparative manner, specifically the Bishop's single effective stress, the independent stress variables approach and the generalized stress framework. The latter considerations lead to the definition of a unified stress context, suitable for modelling soils under different saturation states. In order to qualify the implications brought by the proposed stress framework, several experimental data sets are re‐examined in the light of the generalized effective stress. The critical state lines (CSLs) at different saturation states tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress plane. The effective stress interpretation is also applied to isotropic paths and compared with conventional net stress conception. The accent is finally laid on a second key feature for constitutive frameworks based on a unified stress, namely the sufficiency of a unique mechanical yield surface besides the unique CSL. Copyright © 2007 John Wiley & Sons, Ltd.     

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。     

不同水化状态下的压实膨胀土应力-应变-强度特征

为探讨水化状态对饱和压实膨胀土应力-应变-强度特征的影响,以压实度为95%的荆门弱膨胀土为研究对象,开展了2种典型水化状态下的固结与三轴试验,其中第1种水化状态采用常规饱和方法,第2种水化状态为试样自由膨胀至稳定状态。结果表明：（1）受变形约束条件与渗径的影响,不同水化状态下体膨胀率有较大差别;（2）第2种水化状态下的饱和压实膨胀土具有更大的硬化指数λ与膨胀指数κ、较小的弹性剪切模量,其有效内摩擦角为第1种水化状态下的77.2%,体现出膨胀土饱和强度的变动性;（3）2种水化状态下的固结曲线均呈现出明显的屈服现象,其屈服应力分别为123.2 kPa与94.5 kPa;（4）第1种水化状态下,低围压下试样应变软化与剪胀,高围压下应变强化与剪缩;第2种水化状态下试验围压范围内均发生剪缩和轻微的应变软化;（5）2种水化状态下试样在固结与剪切过程中均表现出超固结性,这种超固结性并非完全由先期固结压力所致,而是试样受荷过程中膨胀受到约束造成的;（6）不同水化饱和状态下初始孔隙比不同,膨胀势也不同,膨胀势与外部约束条件、排水条件、应力状态相互作用,造成其应力-应变-强度特征的差异性。     

Developing a 3D elastoplastic constitutive model for soils: A new approach based on characteristic stress

This paper presents a new approach for the development of an elastoplastic constitutive model to predict the strength and deformation behaviour of soils under general stress conditions. The proposed approach was based on characteristic stress, which considers the effect of the intermediate principal stress on the material strength. Referring to the Cam-clay model, the shear dilatancy equation, plastic potential function and hardening parameter for the developed model were all derived using the characteristic stress. The model predictions indicated that the established model could quantitatively reproduce the negative dilatancy behaviour, positive dilatancy behaviour, and three-dimensional strength properties of soils.