考虑循环软化特性的饱和软土弹塑性本构关系研究

将软化指数关系与非等向硬化模量场理论相结合,研究了可描述循环荷载作用下饱和软土软化特性的增量弹塑性模型。该模型借助硬化模量的插值和映射中心的移动,在偏应力空间中构造硬化模量的演化规则;通过在弹塑性模量插值函数中引入初始弹塑性模量软化系数,模拟循环荷载作用下软土的刚度软化特性;通过引入硬化模量调整系数,增强循环加载时应力-应变曲线的滞回特性;再通过引入反映应变累积速率和大小的模型参数,描述循环加载时软土的应变累积特性。利用Idriss提出的指数关系式近似拟合软化系数随应力循环次数的变化关系,并通过引入循环应力参数建立了循环软化系数与静应力水平和循环应力水平的关系。阐述了确定模型参数的方法,并利用模型预测了相关试验结果,通过预测结果与试验结果的对比,验证了该模型描述循环荷载作用下软土软化特性的可行性。     

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).     

基于Hardin曲线的土体边界面本构模型在ADINA软件中的实现

为了提出一种适合于岩土地震数值模拟的土体本构模型,基于土体动应力-应变关系的Hardin曲线及其在非等幅往返荷载下的Pyke修正,采用von Mises准则在偏应力平面上构造边界面,以反向加载点和当前应力点的连线在边界面上投影的比例作为硬化参数,推导了塑性硬化模量并给出该边界面本构的具体增量表述。在有限元软件ADINA中通过自定义材料的二次开发实现了该本构模型,并利用动三轴试验对该本构模型进行了验证。数值模拟与试验结果的对比表明,本构模型能如实反映土体的应力-应变关系。针对实际工程场地的地震反应,应用边界面本构模型在ADINA中进行了二维数值模拟,与SHAKE91的计算结果进行了对比,说明了该本构模型应用于岩土地震工程问题的合理性。     

A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil

A constitutive model for granular materials is developed within the framework of strain–hardening elastoplasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution. The effects of these irreversible microscopic processes are described macroscopically as accumulated plastic strain. Plastic strain drives the evolution of internal variables which model phenomenologically the changes of mechanical properties induced by grain crushing by controlling the geometry of the yield locus and the direction of plastic flow. An application of the model to Pozzolana Nera is presented. The stress–dilatancy relationship observed for this material is used as a guidance for the formulation of hardening laws. One of the salient features of the proposed model is its capability of reproducing the stress–dilatancy behaviour observed in Pozzolana Nera, for which the minimum value of dilatancy always follows the maximum stress ratio experienced by the material. Copyright © 2002 John Wiley & Sons, Ltd.     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

基于旋转运动硬化理论的修正剑桥模型的改进

修正剑桥模型是最早建立和得到广泛承认的经典土体弹塑性模型之一,但不能模拟应力路径转折时土体的应力-应变特性以及应力引起的各向异性。将旋转运动硬化理论引入到剑桥模型中,给出了椭圆屈服面的旋转运动硬化机制,在不增加任何模型参数的情况下,把等向硬化的修正剑桥模型扩展为旋转运动硬化模型。扩展的新模型既保留了单调加载时的等向硬化的特性,又能反映应力路径转折时土体的本构特性与应力诱发的各向异性,初步验证了模型的有效性。     

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.     

A cyclic elastoplastic-viscoplastic constitutive model for soils

An elastoplastic-viscoplastic constitutive model for soils is presented in this study, based on an original approach concerning viscous modelling. In this approach, the viscous behaviour is defined by internal viscous variables and a viscous yield surface. The model has been developed from a basic elastoplastic model (CJS model) by considering an additional viscous mechanism. The evolution of the viscous yield surface is governed by a particular hardening called ‘viscous hardening’. This model is able to explain the time-dependent behaviour of soils such as creep (primary, secondary and un-drained creep rupture), stress relaxation and strain rate effects in static and cyclic loadings. The existing problems in the classical elasto-viscoplastic models related to the plasticity failure, the rapid loading and the cyclic loading are solved in the proposed model. The physical meanings and the identification strategy of model parameters are clearly given. The validation on certain triaxial test results and the simulation of cyclic triaxial test indicate the capacity of this model in prediction of time-dependent behaviour of clayey soils.     

Nonlinear SEM numerical analyses of dry dense sand specimens under rapid and dynamic loading

The paper mainly concerns the mechanical response of 2D dry dense sand specimens under shock loading. The problem is numerically analysed by means of a SEM dynamic code, within which an already conceived non‐local viscoplastic constitutive model characterized by a non‐associated flow rule and by an anisotropic strain hardening has been implemented. In particular the strain localization and time dependency of the material mechanical response are taken into consideration. Both rapid/static loading and dynamic histories are numerically simulated. In the first case, the time dependency of the material mechanical response can be captured by neglecting inertial effects, while in the second one the two factors are superimposed and the propagation of the stress waves within the specimen is discussed. The interest of these analyses derives from the fact that the diffusion phenomenon takes place within a specimen already localized. Copyright © 2006 John Wiley & Sons, Ltd.     

A double hardening thermo-mechanical constitutive model for overconsolidated clays

On the basis of a double hardening model for clays and available experimental results, a new thermo-elasto-plastic constitutive model for saturated clays is proposed to describe the effects of temperature and overconsolidation ratio on the mechanical properties of saturated clays. Two hardening parameters are introduced: s_c^￠ {\sigma}_{{\rm c}}^{\prime} and α. The proposed model is then applied to simulate the relevant important features of saturated clays with different overconsolidation ratios under different temperature and loading conditions. The model predictions are compared with available experimental results to demonstrate its accuracy and usefulness.     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

Improvement to the intergranular strain model for larger numbers of repetitive cycles

The analysis of geotechnical problems involving saturated soils under cyclic loading requires the use of advanced constitutive models. These models need to describe the main characteristics of the material under cyclic loading and undrained conditions, such as the rate of the pore water pressure accumulation and the stress attractors. When properly doing so, the models are expected to be reliable for their use in boundary value problems. In this work, an extension of the widely implemented intergranular strain model by Niemunis and Herle (Mech Cohes Frict Mater 2(4):279–299, 1997) is proposed. The modification is aimed to improve the capabilities of the model when simulating a number of repetitive cycles, where a proper reduction of the strain accumulation is expected. For validation purposes, the reference model and proposed improvement are compared against some monotonic and cyclic triaxial tests. The results indicate that the intergranular strain improvement model provides a more realistic prediction of the accumulation rates under cyclic loading, without spoiling the advantages of the original formulation.

     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part I—tests with monotonic loading and stress cycles

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such a model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. The purpose of these two companion papers was to provide such database collected for a fine sand. The database consists of numerous undrained cyclic triaxial tests with stress or strain cycles applied to samples consolidated isotropically or anisotropically. Monotonic triaxial tests with drained or undrained conditions have also been performed. Furthermore, drained triaxial, oedometric or isotropic compression tests with several un- and reloading cycles are presented. Part I concentrates on the triaxial tests with monotonic loading or stress cycles. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part II—tests with strain cycles and combined loading

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. It is the purpose of these two companion papers to provide such database collected for a fine sand. Part II concentrates on the undrained triaxial tests with strain cycles, where a large range of strain amplitudes has been studied. Furthermore, oedometric and isotropic compression tests as well as drained triaxial tests with un- and reloading cycles are discussed. A combined monotonic and cyclic loading has been also studied in undrained triaxial tests. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

An Elasto-Plastic Constitutive Model for Rock Joints Under Cyclic Loading and Constant Normal Stiffness Conditions

An elasto-plastic constitutive model is introduced for rock joints under cyclic loading, considering the additional shear resistance generated by the asperity damage in the first forward shear cycle and sliding mechanism for further shearing. A series of cyclic loading direct shear tests was conducted on artificial joints with triangular asperities and replicas of a real rock asperity surface under constant normal stiffness (CNS) conditions. The model was calibrated and then validated using selected data sets from the experimental results. Model simulations were found to be in good agreement with the rock joints behaviour under cyclic loading and CNS conditions both in stress prediction and dilation behaviour. In addition, dynamic stability analysis of an underground structure was carried out, using Universal Distinct Element Code and the proposed constitutive model.     

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。     

Predicting the initiation of static liquefaction of cross‐anisotropic sands under multiaxial stress conditions

Experimental evidence has shown that the liquefaction instability of sands can be affected by its material density, stress state, and inherent anisotropy. In order to predict the initiation of the static liquefaction of inherent cross‐anisotropic sands under multidimensional stress conditions, a rational constitutive model is needed. An elastoplasticity model able to capture the influences of intermediate principal stress ratio (b  = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) and loading direction on stress–strain relationships and volumetric properties was proposed. The yield function was formulated to be controlled by Lode angle, loading direction, and material state; the stress–dilatancy was a material state‐dependent function. After using the existing drained hollow cylinder tests to validate the proposed model, this model was used to simulate the existing undrained hollow cylinder tests. During this simulation, the second‐order work criterion was used to determine the initiation of static liquefaction. The results showed that an increase in both the intermediate principal stress ratio and the loading angle induces a decrease in the second‐order work. Static liquefaction is initiated more easily at a stress state with a large intermediate principal stress ratio and a large loading angle, and the mobilized friction angle at the instability points decreases with the intermediate principal stress ratio and the loading angle. Copyright © 2017 John Wiley & Sons, Ltd.