Kinematic hardening plasticity formulation of small strain behaviour of soils

An objective of this paper is to demonstrate that the small strain model developed by the authors can be incorporated into the conventional kinematic hardening plasticity framework to predict pre‐failure defor mations. The constitutive model described in this paper is constituted by three elliptical yield surfaces in triaxial stress space. Two inner surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third surface is the modified Cam clay large‐scale yield surface. Within the linear elastic region, the soil behaviour is elastic with cross‐coupling between the shear and volumetric stress–strain components. Within the small strain region, the soil behaviour is elasto‐plastic, described by the kinematic hardening rule with an infinite number of loading surfaces defined by the incremental energy criterion. Within the large‐scale yield surface, the soil behaviour is elasto‐plastic, described by kinematic and isotropic hardening of the small strain region boundary. Since the yield surfaces have different shapes, the uniqueness of the plastic loading condition imposes a restriction on the ratio between their semi‐diameters. The model requires 12 parameters, which can be determined from a single consolidated undrained triaxial compression test. Copyright © 2000 John Wiley & Sons, Ltd.     

考虑土体结构性的弹塑性硬化模型

在对人工制备结构性土样等应力比压缩试验结果分析基础上,确定出结构性土体初始屈服面形状和土体初始屈服后塑性应变增量的方向,推导出结构性土体屈服函数的表达式;硬化参数采用塑性功的函数,根据三轴排水剪切试验结果确定出土体的硬化规律。由此构建能反映土体结构性的弹塑性硬化本构模型,并用试验进行了验证。本文提出一种基于试验的建模方法,不依赖经典塑性力学理论的正交流动规则,并建立可考虑土体结构性影响的本构模型,对土体结构性研究具有借鉴意义。     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

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。     

岩土材料应力路径无关硬化参量的构成方法

在分析砂土试验结果的基础上,揭示了基本硬化内参量（塑性体积应变、塑性剪应变）变化的应力路径相关性,提出了应力路径无关硬化参量的一般表达式。并指出了塑性功硬化参量及其提出的黏土和砂土统一硬化参量均是所提一般表达式框架下的特例。还将该统一硬化参量直接和修正剑桥模型结合,并与试验结果对比,表现出描述剪胀特性的简单性和有效性。     

A cap model for partially saturated soils

The present paper deals with the extension of a cap model in order to describe the material behavior of partially saturated soils, in particular, of partially saturated sands and silts. The soil model is formulated in terms of two stress state variables, using net stress and matric suction and, alternatively, the average soil skeleton stress and suction, the latter playing the role of a stress‐like plastic internal variable. The yield surface, consisting of a shear failure surface and a hardening cap surface, the plastic potentials for the non‐associated flow rule and the hardening law for the cap are extended by taking into account the effects of matric suction on the material behavior. Furthermore, the third invariant of the deviatoric stress tensor is taken into account in the formulation of the yield surfaces. The developed model is validated by the numerical simulation of an extensive series of suction controlled tests for a silty sand, which were conducted at different constant values of suction. Although both versions of the soil model yield identical results for stress paths at constant values of matric suction, differences are encountered for stress paths involving wetting. Copyright © 2007 John Wiley & Sons, Ltd.     

New basis for the constitutive modelling of aggregated soils

Natural and compacted soils are usually characterized by aggregation of particles. The mechanical behaviour of these materials depends on soil structure. The oedometric compression tests performed on aggregated samples presented here showed that these materials exhibit a yield limit depending not only on stress history and stress state but also on soil structure. Evidence is provided using the neutron tomography technique. These results revealed that soil structure modification occurs together with plastic deformations. The experimental results are used to propose a new state parameter to quantify the soil structure. Based on pore-scale experimental observations, an evolution law for this parameter is proposed as a function of associated plastic strains. Considering both soil fabric and inter-particle bonding effects, a new yield limit depending on stress state, stress history and soil structure is introduced for the aggregated soils. Accordingly, a new constitutive framework consistent with strain hardening plasticity is proposed to consider soil structure effects in the modelling of aggregated soils.     

含水量对高含冰量冻结砂土屈服面的影响

以往关于冻土屈服特性的研究很少考虑含水量的影响,但实际工程中经常遇到的是变含水量情况,因此本文通过-5.0℃条件下高含冰量冻结砂土的一系列三轴压缩试验,系统地研究了含水量对屈服特性的影响,并且由此建立了带有含水量参数的偏应力-剪应变增量型关系式。试验结果表明：随含水量的变化,应力-应变曲线类型有明显变化,即在不同的含水量区间,含水量对硬化规律有不同的影响特性,因此为了使屈服函数的形式更加简单和提高拟合准确度,对于屈服函数的具体形式应该根据塑性剪应变（硬化参数）和含水量不同区间进行分别确定;当塑性剪应变较小时（0.00%~1.00%）,随含水量的增大,偏应力逐渐增加,而当塑性剪应变较大时（大于1.00%）,随含水量的增大,偏应力有一个先减小后增大的变化过程,并且42.0%可以作为含水量转折点;通过分段硬化原则建立的带有含水量参数的屈服函数与偏应力-剪应变的增量型关系式的模拟值与试验点基本相吻合,这说明得到的屈服函数与偏应力-剪应变的增量型关系式可以用于不同含水量条件下屈服面和偏应力-剪应变曲线的预测。     

Rotational kinematic hardening model for three‐dimensional stress reversals in sand

A kinematic hardening mechanism has previously been proposed to capture the behavior of soil during large stress reversals in the triaxial plane. This mechanism is now extended to the principal stress space. It incorporates rotation and intersection of yield surfaces to achieve a consistent and physically rational fit with experimentally observed soil behavior during large three‐dimensional stress reversals. An existing elasto‐plastic model with isotropic hardening is used as the basic framework to which the rotational kinematic hardening mechanism has been added. The new combined model preserves the behavior of the isotropic hardening model under monotonic loading conditions, and the extension from isotropic to rotational kinematic hardening under three‐dimensional conditions is accomplished without introducing new material parameters. The framework of the model is presented here with some comparisons between theoretical and experimental directions of strain increment vectors to indicate the potential of the model. Copyright © 2008 John Wiley & Sons, Ltd.     

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。     

基于相似性原理超固结土不排水扩张半解析解

在实际工程中,土体往往因卸载、再加载等复杂应力路径而处于超固结状态,而现有的圆孔扩张问题的计算模型往往不能反映超固结土中剪胀、软化等一些特殊性质。为了解决这一问题,基于相似性原理和统一硬化（UH）模型,结合相关联的流动法则和大变形理论,采用相似求解技术求解了超固结土不排水扩张问题的半解析解答。通过理想化算例分析了圆孔扩张挤土产生的应力和孔压响应,并通过分析不同超固结比OCR的土体应力路径的变化规律,讨论了UH模型的适用性。结果表明：对于轻超固结土,空腔周围土体孔压在塑性区沿径向单调递减,随着OCR增大,塑性区内孔压分布呈现出“S”形的趋势,孔壁附近的孔压逐渐减小,孔壁周围甚至出现负孔压。随着OCR增大,压力?扩张曲线收敛变慢。在扩孔过程中正常固结土一直处于剪缩硬化阶段。而对于超固结土,土体则经历了临界状态→剪胀硬化阶段→临界（特征）状态→剪缩硬化阶段。该研究成果不仅丰富了相似求解技术的应用,而且为超固结土中桩基承载力、隧道围岩变形预测和原位测试参数等岩土工程问题的计算提供了理论依据。     

Poroplastic modelling of the excavation and ventilation of a deep cavity

A plastic deviatoric model with hardening is developed on the basis of geomechanical tests performed in the saturated case on low permeable porous material such as argillite. This model is a generalized Mohr–Coulomb plastic criterion combined with a Drucker–Prager plastic potential and the hardening parameter is the plastic distortion. Three different hardening functions have been introduced on the basis of triaxial tests: an increase of friction angle, a decrease of cohesion after a threshold and a contractancy to dilatancy transition for volumetric plastic strain. This plastic model has been adapted to the partially saturated case. The effective stress is expressed thanks to the equivalent interstitial pressure π. Numerical results are presented for the excavation and monotonous ventilation of a deep cylindrical cavity. A first plastification due to excavation is followed by a second one due to desaturation. The extent of the non-saturated zone provokes an extent of a plastic zone in the rock mass. Analysis shows that the origin of the plastification can be found in the deviatoric stresses because mean effective stresses are compressive during drying. Copyright © 2004 John Wiley & Sons, Ltd.     

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semi-analytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.     

Elastic‐plastic solutions for expanding cavities embedded in two different cohesive‐frictional materials

An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large‐strain quasi‐static expansion of both spherical and cylindrical cavities in elastic‐plastic soils is considered. A non‐associated Mohr–Coulomb yield criterion is used for both soils. Closed‐form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground‐freezing around shafts, tunnelling, and mining. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

The influence of the plastic potential on plane strain failure

The influence of the shape of the plastic potential in the deviatoric plane on plane strain collapse is investigated. The most commonly employed elastic‐perfect plastic models are considered, which adopt well‐known failure criteria for defining the yield and plastic potential surfaces, namely the von Mises, the Drucker–Prager, the Tresca, the Mohr–Coulomb and the Matsuoka–Nakai criteria. Finally, the conclusions are also extended to strain hardening/softening models. For simple constitutive models based on perfect plasticity, it is shown that the value of the Lode's angle at plastic collapse in plane strain conditions strongly depends on the specific failure surface adopted for reproducing the plastic potential surface. If the value of the Lode's angle at yield coincides with the failure value prescribed by the plastic potential, the stress–strain curves exhibit the typical perfect plastic behaviour with yield coinciding with failure, otherwise the stress changes after yield and the stress‐strain curves resemble those of strain hardening/softening models. The infinite strength which is in some situations exhibited by the Drucker–Prager model in plane strain condition is investigated and explained, and it is shown that this can also affect strain hardening/softening models. Copyright © 2013 John Wiley & Sons, Ltd.     

Generalized strain probing of constitutive models

Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.     

近代海积软土结构性及弹-塑性模型研究

土的结构性数学模型是 2 1世纪土力学的核心问题。本文分析了近代海积软土的结构性以及其塑性体应变硬化和塑性偏应变硬化的机制 ,建立了弹塑性本构模型 ,模型采用了具有双硬化参数的屈服轨迹及含结构性参数 m的塑性应变方程。     

基于能量耗散的球孔扩张理论解答

以空间准滑动面（SMP）准则为基础,推导了扩底桩扩孔压力的理论解。从能量耗散的角度分析球孔扩张的全过程,利用应力不变量推导了符合球孔扩张的屈服准则;化简微分方程得到了弹塑性区应力表达式,进而求出位移、应变表达式;分别利用体积守恒和能量守恒性推导出扩孔压力的表达式。该法考虑了塑性区弹性变形,并得到了扩孔压力p、塑性区半径R与扩孔半径a的关系。算例分析表明,该方法计算的扩孔压力与现场试验得出的结果较好地吻合,塑性区半径和扩孔压力均随扩孔半径的增加而增大,但增幅逐渐减小而趋于稳定值,剪胀角对塑性区半径和扩孔压力影响显著,随着剪胀角的增加,塑性区半径和扩孔压力明显增加。     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.