基于广义塑性力学的土体次加载面循环塑性模型(Ⅱ):本构方程与验证

按广义塑性力学原理，导出了土体次加载面循环塑性模型的本构方程，建立了相应的加卸载准则以及模型参数的确定方法。通过多种应力路径下土的本构响应的模拟，表明次加载面循环塑性模型能较好地反映循环荷载作用下土体呈现的非线性、滞回性与变形的积累性三方面主要特征，初步验证了模型的有效性。     

Automatic substepping integration of the subloading tij model with stress path dependent hardening

This paper discusses the numerical integration of the subloading tij model. This is an elastoplastic model with stress path dependent hardening, which can predict the behaviour of normally consolidated clays or loose sands, as well as of over-consolidated clays or dense sands, with a small number of material parameters. Three features distinguish the subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor t_ij; (b) the split of the plastic strain increments in two components leading to a stress path dependent hardening; and (c) the use of two yield surfaces (subloading yield surface and normal yield surface). This last feature is based on the concept of sub-yielding stress states and adds an extra internal strain-like hardening variable, related to the relative density state, which demands its own evolution law. The three characteristics above greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam clay model, at the cost of only two additional parameters. Nonetheless, the numerical integration of the constitutive equations of subloading tij model is a bit challenging, mainly due to the stress path dependent hardening. In order to integrate the equations of subloading tij model in the same way as for any conventional model, the authors reformulated its equations in a simpler and direct manner. Here, these equations are integrated using multi-step explicit schemes, such as modified-Euler and Runge–Kutta–Dormand–Price, with automatic error control. Simple forward-Euler scheme is also used for the sake of comparison. The results show that the modified-Euler scheme is more accurate as well as faster than the other schemes analysed over a wide range of error tolerance. Besides, the automatic feature of these schemes is a great convenience for the users of numerical codes.     

基于次加载面理论改进的ALPHA模型及其数值实施

基于次加载面理论对ALPHA模型进行了改进,并在模型中考虑了土体初始各向异性;提出了与模型相适应的半隐式本构积分算法,据此在通用有限元软件ABAQUS平台上开发了相应的用户材料子程序;利用建立的计算程序,对不同排水条件的三轴试验进行了数值模拟。与已有研究成果对比表明,提出的半隐式本构积分算法,可较好地实现复杂本构模型的数值实施。改进的本构模型克服了修正剑桥模型预测的超固结土峰值强度过高、初始屈服面内假定为弹性变形等缺点,能够较好地描述土体初始屈服面内的的非线性和不可恢复性变形特征;通过变化模型参数,可模拟变形特性较为复杂的土体。     

The subloading isotropic plasticity as a variable modulus model

The subloading concept is an extension of mathematical plasticity which defines an internal surface to the conventional yield surface. It is indeed a versatile approach, especially for the modelling of soils under quasi-static cycles with smooth transitions from pure elastic to elastoplastic behaviour. For the case of isotropic hardening models, this paper demonstrates that the subloading isotropic plasticity is equivalent to a variable modulus approach and therefore a simpler and equivalent methodology can be adopted instead. In addition to demonstrating this equivalence, an alternative formulation that was presented elsewhere and that uses only one surface is briefly discussed. The alternative formulation can then be easily applied to popular models for soils such as the Cam clay model. Finally, some numerical predictions are presented in order to illustrate the capabilities of the subloading isotropic plasticity and the corresponding variable modulus approach.     

软粘土的各向异性和小应变条件下的本构模型(ASM)

以能量方程为基础推导出各向异性和小应变条件下弹塑性的本构方程,并将屈服面与修正桥模型和试验测得的屈服面进行了对比,表明新的屈服面比修正剑桥模型更接近试验结果,采用从初始应力到状态边界面的距离为参数的系数来修正硬化准则以模拟土体小应谱条件下的应力－应变特征。将新的本构模型编入有限元程序,对小应变试验进行了计算分析,计算结果表明,新的模型比修正剑桥模型能更好地反映土体的主要力学特性。     

A viscoplastic subloading soil model for rate‐dependent cyclic anisotropic structured behaviour

This paper presents a new purely viscoplastic soil model based on the subloading surface concept with a mobile centre of homothety, enabling the occurrence of viscoplastic strains inside the yield surface and avoiding the abrupt change in stiffness of the traditional overstress viscoplastic models. This is required for overconsolidated soils. The model is formulated to reproduce the soil rate‐dependent behaviour under cyclic loading (changes in loading direction) and incorporates both initial and induced anisotropy, as well as destructuring. The model shows good qualitative response to some imposed three‐dimensional stress paths under quasi‐inviscid (elastoplastic) behaviour. Some of the main time‐dependent aspects of soil behaviour that the model is capable of reproducing were also illustrated. The capability of the model to adequately reproduce the results from an undrained triaxial test performed on stiff overconsolidated clays from the Lisbon region (Formação de Benfica), with an unloading–reloading deviatoric stress cycle at constant mean stress, that incorporates a series of staggered fast loading and creep stages, was evaluated. The model was able to reproduce well the main observed aspects of the time‐dependent stress–strain response and pore pressure evolution of a stiff overconsolidated clay under complex loading. The revised and generalised viscoplastic subloading surface concept is viable and can be applied to a consistent extension to viscoplasticity, including in the interior of the yield surface, of existing elastoplastic models formulated for soils and other materials. Copyright © 2016 John Wiley & Sons, Ltd.     

基于广义塑性力学的土体次加载面循环塑性模型(Ⅰ): 理论与模型

简要地介绍了次加载面理论的基本思想、假设及其物理解释。在广义塑性力学的框架内，引入次加载面的思想，把常规的椭圆-抛物线双屈服面模型，扩展为次加载面循环塑性模型，以反映循环荷载作用下土体的曼辛效应与棘轮效应。模型能考虑塑性应变增量对应力增量的相关性，既能反映土体的循环加载特性，又能反映正常固结土和超固结土的单调加载特性。     

Rational approach to anisotropy of sand

The paper presents a constitutive model for the three-dimensional deformation–strength behaviour of inherently anisotropic sand. Based on non-linear tensorial functions, the model is developed without recourse to the concepts in plasticity theory such as yield surface and plastic potential. Benefited from the fact that no decomposition of strain into elastic and plastic parts is assumed, a unified treatment of anisotropic behaviour of deformation and strength is achieved. Anisotropy is characterized by a vector normal to the bedding plane. The extension of the constitutive model is furnished by incorporating the vector under consideration of the principle of objectivity and the condition of material symmetry. Distinct features of the model are its elegant formulation and its simple structure involving few material parameters. Model performance and comparison with experiments show that the model is capable of capturing the salient behaviour of anisotropic sand. © 1998 John Wiley & Sons, Ltd.     

基于上下负荷面的弹黏塑性本构模型及应力积分算法实现

为了描述天然软土的时间相依以及结构性特征,提出了一种能考虑土体超固结和结构性的实用弹黏塑性本构模型。它以Asaoka和Hashiguchi的上下负荷面作为某一应变速率下的参考屈服面,按照相对过应力的基本思路,新引入了两个能通过不同应变速率三轴压缩试验测定的率敏性参数 和 ,建立了以当前应力、黏塑性应变以及黏塑性应变速率为状态变量的动屈服准则函数,并给出了基于Newton-Raphson迭代的应力积分算法,且成功地将其嵌入到大型有限元软件ABAQUS中。最终通过数值算例来验证模型的正确性以及应力积分算法的可靠性。结果表明：该模型能同时描述土体的率敏性、蠕变以及结构性特征,模型参数物理意义明确、易懂可测,预测结果与试验数据吻合良好,可用于复杂边值问题的有限元计算。     

Explicit integration of a porosity‐dependent hydro‐mechanical model for unsaturated soils

An adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ –Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ –Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ –Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ –Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ –Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

考虑冻融循环的季冻区高等级公路路基填土本构模型研究

在季冻区高等级公路路基场地取土,制成重塑土试件进行冻融循环试验。而后对经历不同冻融循环次数的土体进行三轴固结排水（CD）剪切试验,测得应力、应变数据。在大量试验数据的基础上,遵循岩土本构变化规律,以岩土弹塑性力学为理论基础,在p-q空间,以椭圆方程拟合体变屈服面,以抛物线方程拟合剪切屈服面,采用塑性关联流动,得到考虑冻融循环条件下融土的弹塑性本构方程。通过编程计算后,对比计算与试验结果,证明该双屈服面本构模型能够较为准确地预估冻融循环土体的应力-应变关系,该本构模型对季冻区路基土体长期稳定性分析和工程预测具有重要参考意义。     

卸荷条件下岩石变形特征及本构模型研究

基于岩石试件的卸荷试验,研究了卸荷条件下岩石的应力—应变全过程曲线和破裂特征,研究表明：卸荷过程中岩石向卸荷方向回弹变形强烈、扩容显著、脆性破坏特征明显;卸荷条件下岩石破坏具有较强的张性破裂特征,各种级别的张裂隙发育,其剪性破裂面追随张拉裂隙发展。基于试验认识,将卸荷条件下岩石的本构模型分为4段：弹性段、卸荷屈服段、峰后脆性段及残余理想塑性段;通过体积应变εv将Griffith和Mohr Coulomb屈服准则结合起来,建立卸荷条件下岩石的屈服准则,并在应变空间建立相应的卸荷非线性屈服段本构方程;运用应变软化理论,建立卸荷岩石峰后脆性段本构方程。     

基于广义位势理论的类剑桥模型

广义位势理论直接从数学原理出发建立本构模型,避开了传统塑性理论中塑性势函数等复杂概念,为研究岩土本构模型提供了新的思路。基于广义位势理论中土的应力空间多重势面模型,对剑桥模型“能量方程假设”的数学原理进行分析,从数学角度上建立了一个改进的剑桥模型（即类剑桥模型）,而修正剑桥模型等可作为其特例。利用不同应力路径下的试验数据对其合理性进行验证,并与剑桥模型进行对比分析。结果表明：类剑桥模型的参数确定方便、自由,计算结果与试验较一致,甚至优于修正剑桥模型;类剑桥模型所采用的数学原理更明确,且避免了确定塑性势函数和能量方程的困难及其所带来的误差,是一个具有较好实用价值的模型。     

基于广义位势理论的接触面本构模型一般表述

基于广义位势理论建立的岩土体材料本构模型以及岩土体材料与结构接触面本构模型原理相通,只是前者是在三轴剪切试验条件下的三维应力空间建模,后者是在单剪试验条件下的二维应力空间建模。单剪试验条件下土与结构的接触面问题可以看作是法向与切向应力空间上的二维问题,其试验结果可以表达成由应力、应变组成的二维矢量。结合接触面力学特性,确定应力空间中的势函数以及塑性状态方程,可以推导出双重势面接触面弹塑性本构方程的一般表达式。进一步取两个势函数分别为法向应力和切向应力,建立简化双重势面接触面弹塑性模型的本构方程,该方程可直接应用于有限元等数值分析。结合试验实例对建模方法的合理性进行验证,模型拟合效果良好。研究结果表明,基于广义塑性位势理论建立接触面本构模型无需推求塑性势函数和屈服函数,可以直接得到弹塑性刚度矩阵,且建模方便。     

An elastoplastic strainhardening model for soil allowing for hydraulic bonding–debonding effects

The paper presents a strainhardening constitutive model for unsaturated soil behaviour based on energy conjugated stress variables in the framework of superposed continua. The proposed constitutive law deals with hydro‐mechanical coupling phenomena. The main purpose is to develop within a consistent framework a model that can deal with possible mechanical instabilities occurring in partially saturated materials. The loss of capillary effects during wetting processes can, in fact, play a central role in unstable processes. Therefore, it will be shown that the bonding effects due to surface tensions can be described in a mathematical framework similar to that employed for bonded geomaterials to model weathering or diagenesis effects, either mechanically or chemically induced. The results of several simulations of common laboratory tests on partially saturated soil specimens are shown. The calculated behaviour appears to be in good qualitative agreement with that observed in the laboratory. In particular it is shown that volumetric collapse phenomena due to hydraulic debonding effects can be successfully described by the model. Finally, it will be highlighted the ability of the model to naturally capture the transition to a fully saturated condition and to deal with possible mechanical instabilities in the unsaturated regime. Copyright © 2008 John Wiley & Sons, Ltd.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

基于统计损伤本构模型的改进桩-土接触面模型研究

建立准确合理的接触面本构模型是研究桩基承载力、沉降及变形等问题的前提。考虑桩-土界面初始剪切刚度的深度效应,提出基于统计损伤本构模型的无厚度接触面本构模型,根据剪切试验的数据对改进的接触面本构模型参数进行拟合,得到了不同法向应力下的模拟曲线。利用FLAC3D软件内嵌的FISH语言,对桩-土界面进行改进本构模型的二次开发,提出的无厚度接触面模型合理地模拟出桩-土界面刚度的非线性,成功实现了桩-土剪切试验过程的数值模拟。计算结果表明：提出的无厚度接触面本构模型能够合理地模拟桩-土界面的力学行为,可以描述接触面刚度的非线性变化,也适于程序化计算,拓展了接触面统计损伤本构模型的应用领域,为深入探讨桩基承载变形性状奠定了基础。     

孔隙液体的可压缩性对非饱和孔隙介质弹塑性分析的影响

首先在多相孔隙介质的混合物理论框架内探讨了如何利用固-液两相孔隙介质模型描述介质的非饱和问题。其次,讨论了一个实用的描述孔隙液体可压缩性的方法,并建立了小变形条件下固-液两相孔隙介质的弹塑性本构方程。最后,采用俞茂宏统一强度理论,针对一个具体的结构例子,分析了孔隙液体的可压缩性对结构弹塑性分析的影响。     

Diffuse bifurcations engraving diverse shear bands in granular materials

Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam‐clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was reformulated to be compatible with the multiplicative hyperelasto‐plasticity for finite strains. This enhanced constitutive model was implemented into a finite‐element code reinforced by a stress updating algorithm based on the return‐mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond‐ and column‐like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which broke out‐of‐plane uniformity and led to 3‐dimensional diamond‐like patterns, were detected. Diffuse bifurcations, which were difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns.