A two-surface plasticity model for stiff clay

This paper presents a constitutive model for describing some important features of the behavior of natural stiff clay evidenced experimentally such as the limited elastic zone, the presence of strain hardening and softening, and the smooth transition from elastic behavior to a plastic one. The model, namely ACC-2, is an adapted Modified Cam Clay model with two yield surfaces: similarly to bounding surface plasticity theory, an additional yield surface—namely Inner yield surface—was adopted to account for the plastic behavior inside the conventional yield surface. A progressive plastic hardening mechanism was introduced with a combined volumetric-deviatoric hardening law associated with the Inner yield surface, enabling the plastic modulus to vary smoothly during loading paths. The main feature of the proposed model is that its constitutive equations can be simply formulated based on the consistency condition for the Inner yield surface, so that it can be efficiently implemented in a finite element code using a stress integration scheme similar to that of the Modified Cam Clay model. Furthermore, it is proved to be an appropriate model for natural stiff clay: the simulations of a set of tests along different mechanical loading paths on natural Boom Clay show good agreement with the experimental results.     

泥岩弹塑性损伤本构模型及其参数辨识

以连续介质力学和不可逆热力学为基础,将损伤引入到修正的Mohr-Coulomb准则中,建立了泥岩弹塑性损伤本构模型反映泥岩软硬化行为,通过构建损伤势函数导出了泥岩的损伤演化方程,编制了泥岩弹塑性损伤本构模型及其参数反演程序。并根据非排水条件下泥岩三轴试验结果,采用多目标函数优化反分析法获得了泥岩本构模型参数。研究成果表明,所提出的弹塑性损伤本构模型能有效地描述泥岩在不同应力状态下的力学特性。     

循环荷载作用下饱和软黏土的损伤模型

基于各向同性弹塑性损伤和Prevost模型的基本理论,把弹塑性等向硬化、运动硬化和各向同性损伤结合起来,推导了循环荷载作用下不排水饱和软黏土的弹塑性动力损伤本构模型。由循环累积塑性偏应变建立损伤演化方程,以描述循环加载对软黏土结构的破坏作用,并通过对循环三轴试验的模拟验证了模型的有效性。结果表明,提出的模型能较好地描述饱和软黏土在循环荷载作用下的变形、孔压变化及模量损伤过程。     

An elastoplastic model with combined isotropic–kinematic hardening to predict the cyclic behavior of stiff clays

This paper presents a kinematic hardening model for describing some important features of natural stiff clays under cyclic loading conditions, such as closed hysteretic loops, smooth transition from the elastic behavior to the elastoplastic one and changes of the compression slope with loading/unloading loops. The model includes two yield surfaces, an inner surface and a bounding surface. A non-associated flow rule and a kinematic hardening law are proposed for the inner surface. The adopted hardening law enables the plastic modulus to vary smoothly when the kinematic yield surface approaches the bounding surface and ensures at the same time the non-intersection of the two yield surfaces. Furthermore, the first loading, unloading, and reloading stages are treated differently by applying distinct hardening parameters. The main feature of the model is that its constitutive equations can be simply formulated based on the consistency condition for the inner yield surface based on the proposed kinematic hardening law; thereby, this model can be easily implemented in a finite element code using a classic stress integration scheme as for the modified Cam Clay model. The simulation results on the Boom Clay, natural stiff clay, have revealed the relevance of the model: a good agreement has been obtained between simulations and the experimental results from the tests with different stress paths under cyclic loading conditions. In particular, the model can satisfactorily describe the complex case of oedometric conditions where the deviator stress is positive upon loading (compression) but can become negative upon unloading (extension).     

A two‐surface thermomechanical model for saturated clays

This paper presents an advanced thermomechanical model – TEAM in the framework of two‐surface plasticity for saturated clays, with emphasis put on some important thermomechanical features of natural clays evidenced experimentally such as the limited thermomechanical elastic zone, the smooth transition from elastic to plastic behavior. Two plastic mechanisms are introduced in the model: one is to reproduce the thermoplasticity involving thermal expansion and contraction observed at high over‐consolidation ratios and the second one describes the temperature effect on the yield behavior. The model adopts additional yield surfaces, namely inner yield surfaces that are associated with the two proposed plastic mechanisms to account for the plastic behavior inside the existing conventional thermomechanical yield surface namely yield surfaces. The general expressions of the yield surfaces and plastic potentials in p′–q–T space are introduced. A progressive plastic hardening mechanism associated with the inner yield surface is defined, enabling the plastic modulus to vary smoothly during thermomechanical loadings inside the yield surfaces. Several tests on natural Boom clay along different thermomechanical loading paths have been simulated by TEAM, and results show its relevance in describing the thermomechanical behavior of saturated clays. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of yielding and stress–stain behavior of shanghai soft clay

In this paper, a simple bounding surface plasticity model is used to reproduce the yielding and stress–strain behavior of the structured soft clay found at Shanghai of China. A series of undrained triaxial tests and drained stress probe tests under isotropic and anisotropic consolidation modes were performed on undisturbed samples of Shanghai soft clay to study the yielding characteristics. The degradation of the clay structure is modeled with an internal variable that allows the size of the bounding surface to decay with accumulated plastic strain. An anisotropic tensor and rotational hardening law are introduced to reflect the initial anisotropy and the evolution of anisotropy. Combined with the isotropic hardening rule, the rotational hardening rule and the degradation law are incorporated into the bounding surface formulation with an associated flow rule. Validity of the model is verified by the undrained isotropic and anisotropic triaxial test and drained stress probe test results for Shanghai soft clay. The effects of stress anisotropy and loss of structure are well captured by the model.     

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.     

基于微观力学机制的各向异性结构性砂土的本构模型研究

在岩土破损力学基础上,基于微观破损机制,提出了考虑各向异性的结构性砂土本构理论。采用Lade-Duncan强度准则考虑中主应力对抗剪强度的影响;采用考虑颗粒排列组构的各向异性状态变量A反映各向异性对土体强度和变形的影响;通过相似扩大重塑土的屈服面反映结构性对土性的影响;通过引入非相关联流动法则考虑各向异性和结构性对土体塑性变形的影响。同时,将基于微观力学机制的损伤演化规律引入结构性土的硬化规律;该硬化规律同时考虑了塑性体积应变和剪切应变对各向异性结构性土强度的影响。然后将该模型用于模拟室内三轴压缩试验,初步验证了该模型的合理性和适用性。     

软黏土的各向异性临界状态模型

剑桥模型只适用于正常固结软黏土,不能描述不等向固结土的应力-应变行为的各向异性特性。基于剑桥模型,在其椭圆屈服面中引入各向异性张量和一个形状参数,建立了一个各向异性屈服面,提出了一个适用于等向和不等向固结软黏土的本构模型。各向异性张量的初始值由初始固结应力状态确定,其演化过程由一个与塑性剪应变和塑性体应变都有关的硬化法则描述。形状参数的引入保证了各向异性屈服面的灵活性和适应性。通过对Boston Blue黏土、高岭土和Otaniemi黏土的三轴试验结果的模拟,验证了模型的模拟能力。     

Hollow Cylinder Tests on Boom Clay: Modelling of Strain Localization in the Anisotropic Excavation Damaged Zone

Boom Clay is extensively studied as a potential candidate to host underground nuclear waste disposal in Belgium. To guarantee the safety of such a disposal, the mechanical behaviour of the clay during gallery excavation must be properly predicted. In that purpose, a hollow cylinder experiment on Boom Clay has been designed to reproduce, in a small-scale test, the Excavation Damaged Zone (EDZ) as experienced during the excavation of a disposal gallery in the underground. In this article, the focus is made on the hydro-mechanical constitutive interpretation of the displacement (experimentally obtained by medium resolution X-ray tomography scanning). The coupled hydro-mechanical response of Boom Clay in this experiment is addressed through finite element computations with a constitutive model including strain hardening/softening, elastic and plastic cross-anisotropy and a regularization method for the modelling of strain localization processes. The obtained results evidence the directional dependency of the mechanical response of the clay. The softening behaviour induces transient strain localization processes, addressed through a hydro-mechanical second grade model. The shape of the obtained damaged zone is clearly affected by the anisotropy of the materials, evidencing an eye-shaped EDZ. The modelling results agree with experiments not only qualitatively (in terms of the shape of the induced damaged zone), but also quantitatively (for the obtained displacement in three particular radial directions).     

泥岩隧道施工过程中渗流场与应力场全耦合损伤模型研究

在连续损伤力学理论基础上,将塑性损伤演化及渗流相互耦合的概念引入Mohr-Coulomb 破坏准则,用于分析在孔隙压力和塑性损伤演化共同作用下岩石损伤演化机制,建立了相应的有限元损伤数值分析模型,并应用于比利时核废料库开挖过程中泥岩隧道附近围岩发生损伤演化、渗流场和应力场耦合过程分析中,得到了开挖引起的围岩损伤特性、孔隙压力以及渗透性的变化规律,为进一步研究隧道流变过程水力耦合特性合理的数值计算模型建立方法提供基础。     

描述饱和黏性土应变软化的弹塑性双面模型

常规三轴压缩试验中具有较强结构性的黏性土在围压较低时其应力−应变关系会呈现应变软化现象,一般还伴有塑性变形,通常土体内部结构损伤是应变软化产生的主要原因。考虑到采用经典塑性理论描述材料的应变软化不仅会违背 Drucker 的稳定性假设,而且也不能描述卸载塑性。因此,基于修正剑桥模型及 Li 和 Meissner 提出的塑性硬化准则,建立了一个描述饱和黏性土不排水应变软化的弹塑性双面模型。该模型以应力−应变曲线的峰值点分界,将应变硬化和应变软化分别作为独立的加载事件进行分析,同时引入新的结构性参数表征剪切过程中土体结构损伤导致的塑性刚度衰退。对不同固结状态饱和结构性黏土的三轴固结不排水压缩试验结果的模拟表明,所建模型能够较好地描述饱和黏性土的不排水应变软化特性。     

考虑循环载荷下饱和黏土软化的损伤边界面模型研究

研究表明,循环载荷作用下饱和黏土将发生软化,其机制主要有两个：一是孔压的积累;二是土体原有结构的不断损伤和新结构的不断重塑。针对上述机制,基于广义各向同性硬化准则建立了考虑饱和黏土循环软化的损伤单面模型。该模型在有效应力空间中引入损伤变量,表征土体结构的损伤和重塑程度,在连续的循环加载下,损伤不断累积,边界面则随着损伤的累积不断收缩,以模拟饱和黏土刚度和强度的软化;以应力反向点作为边界面的广义各向同性硬化中心和映射法则的映射中心,灵活地选择塑性模量的插值公式以模拟塑性变形和孔压的累积以及应力-应变的滞回特性。应用该模型对不排水循环三轴试验进行模拟,并且考查了循环周次、循环应力水平和固结历史对饱和黏土循环软化特性的影响,并与相关试验比较,验证了模型的有效性。     

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。     

A micro-mechanics-based elastic–plastic model for porous rocks: applications to sandstone and chalk

A micro-mechanics-based elastic–plastic model is proposed to describe mechanical behaviors of porous rock-like materials. The porous rock is considered as a composite material composed of a solid matrix and spherical pores. The effective elastic properties are determined from the classical Mori–Tanaka linear homogenization scheme. The solid matrix verifies a pressure-dependent Mises–Schleicher-type yield criterion. Based on the analytical macroscopic yield criterion previously determined with a nonlinear homogenization procedure (Shen et al. in Eur J Mech A/Solids 49:531–538, 2015), a complete elastic–plastic model is formulated with the determination of a specific plastic hardening law and plastic potential. The micro-mechanics-based elastic–plastic model is then implemented for a material point in view of simulations of homogeneous laboratory tests. The proposed model is applied to describe mechanical behaviors of two representative porous rocks, sandstone and chalk. Comparisons between numerical results and experimental data are presented for triaxial compression tests with different confining pressures, and they show that the micro-mechanical model is able to capture main features of mechanical behaviors of porous rock-like rocks.     

Multiscale modeling of a sensitive marine clay

This paper examines the mechanical behavior of a sensitive marine clay. Various laboratory tests on intact and reconstituted samples of Guinea Gulf marine clay were performed under isotropic compression and drained triaxial compression at constant confining stresses. Microstructure analysis on intact and reconstituted samples was also carried out under different loading conditions. The effect of inter‐aggregates bonding on mechanical properties is discussed. Based on experimental analysis, a new modeling method is proposed. In this approach, the clay is regarded as an assembly of aggregates of clay particles. An inter‐aggregate contact law is introduced relating contact forces to aggregates relative displacements. The deformation of the assembly can be obtained by integrating the movement of the inter‐aggregate contacts in all orientations. Thus, the effect of inter‐aggregates bonds and debonding is considered in a direct way. The model is evaluated through comparisons between the predicted and measured results on Guinea Gulf marine clay. The evolutions of local stresses, strains, and bonds in inter‐aggregates planes are discussed to explain the anisotropy induced by the applied loading. Copyright © 2010 John Wiley & Sons, Ltd.     

Single hardening constitutive model for frictional materials III. Comparisons with experimental data

A unified constitutive model for the behavior of frictional materials is described. The model is based on concepts from elasticity and plasticity theories. In addition to Hooke's law for the elastic behavior, the framework for the plastic behavior consists of a failure criterion, a nonassociated flow rule, a yield criterion that describes contours of equal plastic work, and a work-hardening/softening law. The functions that describe these components are all expressed in terms of stress invariants. The model incorporates twelve parameters which can all be determined from simple experiments such as isotropic compression and conventional triaxial compression tests. Validation of the model is achieved by comparison of predicted and measured stress-strain curves for various two- and three-dimensional stress-paths obtained for different types of frictional materials.     

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.     

考虑温度影响的冻土蠕变本构模型

冰作为冻土的基本组成部分,对冻土蠕变的加速蠕变阶段有重要影响。温度通过影响冻土中冰的冻结与融化过程,及其黏塑性流动,引起冻土结构的强化与弱化,从而成为了决定冻土蠕变力学行为的关键因素之一。同时,外部应力也造成冻土的强化与弱化,影响着冻土的蠕变。通过引入硬化因子与损伤因子来考虑温度、应力造成的冻土材料强化与弱化。硬化因子H代表了蠕变过程中强化效应的大小,而损伤因子D则代表了由弱化效应造成的冻土材料相关参数的折减比例,进而提出了适用于冻土的改进西原蠕变本构模型。该模型预测值与试验数据的比较表明：改进的模型不仅能较好地描述初始蠕变阶段、稳定蠕变阶段,而且相比于传统模型,能更好地描述冻土加速蠕变阶段,具有合理性与一定的实用性。     

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。