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。     

Constitutive description of interface behavior including cyclic loading and particle breakage within the framework of critical state soil mechanics

The cyclic behavior of soil–structure interface can be very important in dynamic problems. The cyclic behavior of soil–structure interface may be nonlinear, which includes hysteresis, hardening, degradation, and particle breakage. The breakage of granular soil particles during shearing of granular soil–structure interface is associated with cyclic degradation and can be critical to the dynamic behavior of soil–structure system. The critical state soil mechanics concept formerly used to simulate the nonlinear monotonic behavior of granular soil–structure interface was modified and extended to describe the cyclic behavior, especially soil‐particle breakage and degradation during cyclic shearing. Soil‐particle breakage was assumed to relate to the energy consumption during cyclic shearing and the critical state line of the soil–structure interface was assumed to translate with the consumption of shearing energy during cyclic shearing as the threshold value is attained. The model was formulated in the framework of generalized plasticity and is capable of describing the salient features of granular soil–structure interface under cyclic loading. Most of the model parameters have straightforward physical meanings and are calibrated using monotonic or cyclic interface test results. The proposed model was calibrated and validated against published test results. The dependency of interface behavior on stress path and cyclic degradation can be successfully described by the proposed model. Copyright © 2008 John Wiley & Sons, Ltd.     

A cyclic elastoplastic constitutive model and effect of non-associativity on the response of liquefiable sandy soils

A large number of constitutive models for geomaterials, such as soils and rocks, have been proposed over the last three decades. Those models have been implemented into computer codes and have been successfully used to solve practical engineering problems particularly under monotonic loading conditions. Compared with the models for monotonic loadings, more improvements for cyclic models are necessary in order to obtain more accurate predictions for the dynamic behavior of geomaterials, e.g., the behavior during earthquakes. A cyclic elastoplastic model has been developed in this study for sandy soils; it is based on the kinematical hardening rule with a yield function that includes the changes in the stress ratio and the mean effective stress considering the degradation of the yield surface. From a simulation with the present model, it has been found that strong non-associativity leads to a large decrease in the mean effective stress during cyclic deformations under undrained conditions, while the model with the associated flow rule does not. This result is quite important because the mean effective stress becomes almost zero at the state of full liquefaction. Compared with the experimental results, the model can accurately reproduce the cyclic behavior of soil.     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

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。     

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).     

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.     

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.     

循环荷载下非饱和结构性黏土的弹塑性双面模型

非饱和黏土的结构性能够显著影响其力学特性。基于非饱和土经典模型BBM（Barcelona basic model）和一种可描述循环塑性的硬化法则,引入体积破损率的作为标准土体结构破损的参数,建立了一个描述常吸力下非饱和结构性黏土静态及动态力学特性的弹塑性双面模型。模型在应力空间中包含与重塑非饱和土屈服面几何相似的结构性边界面和加载面,采用径向映射法则和可移动的记忆中心原理,通过结构性边界面和加载面在应力空间中的演化来反映循环加载过程中非饱和结构性黏土的循环塑性特征和结构损伤过程。通过与相关非饱和黏土控制吸力试验数据的比较,表明该模型能够较好地反映静态加载下非饱和结构性黏土的力学特性,而模型预测的循环荷载下的应力?应变特征也具有一定的合理性。     

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.     

A multisurface kinematic hardening model for the behavior of clays under combined static and undrained cyclic loading

In dynamic geotechnical problems, soils are often subjected to a combination of sustained static and fast cyclic loading. Under such loading conditions, saturated and normally consolidated clays generally experience a build-up of excess pore water pressure along with a degradation of stiffness and strength. If the strength of the soil falls below the static stress demand, a self-driven failure is triggered. In this paper, a constitutive model is presented for the analysis of such problems, based on a general multisurface plasticity framework. The hardening behavior, the initial arrangement of the surfaces, and the nonassociated volumetric flow rule are defined to capture important aspects of cyclic clay behavior. This includes nonlinear hysteretic stress-strain behavior, the effect of anisotropic consolidation, and the generation of excess pore water pressure during undrained cyclic loading along with a degradation of stiffness and strength. The model requires nine independent parameters, which can be derived from standard laboratory tests. A customized experimental program has been performed to validate the model performance. The model predictions show a good agreement with test results from monotonic and cyclic undrained triaxial tests, in particular with respect to the strain-softening response and the number of loading cycles to failure. A procedure for a general stress-space implicit numerical implementation for undrained, total stress-based finite element analyses is presented, including the derivation of the consistent tangent operator. Finally, a simulation of the seismic response of a submarine slope is shown to illustrate a possible application of the presented model.     

上海软土动剪切模量衰减规律的试验研究

为了获得上海软土在循环动力荷载作用下的动力特性,特别是动剪切模量的衰减规律,采用原状第④层上海软土进行等向固结不排水动三轴试验,分析了加载频率和动应力比 对动剪切模量的影响。试验结果表明,对于上海第④层软土,动应力比达到0.2时,土样才发生破坏;土样的剪切模量-累积轴应变曲线不受加载频率和动应力比的影响;剪切模量的衰减下降主要发生在轴应变0～1%区间。最后提出了一个描述剪切模量衰减规律的数学模型。     

A multi‐mechanism constitutive model for plastic adaption under cyclic loading

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi‐mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain‐hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical Study of Behavior of Circular Footing on Geogrid-Reinforced Sand Under Static and Dynamic Loading

A series of axi-symmetry models using finite element analyses were performed to investigate the behavior of circular footings over reinforced sand under static and dynamic loading. Geogrid was modeled as an elastic element and the soil was modeled using hardening soil model which use an elasto-plastic hyperbolic stress–strain relation. Several parameters including number of geogrid layers, depth to the first geogrid layer, spacing between layers and load amplitude of dynamic loading are selected in this paper to investigate the influence of these parameters on the performance of reinforced systems under both static and dynamic loads. The numerical studies demonstrated that the presence of geogrid in sand makes the relationship between contact pressure and settlement of reinforced system nearly linear until reaching the failure stage. The rate of footing settlement decreases as the number of loading cycles increases and the optimum values of the depth of first geogrid layer and spacing between layers is found 20% of the footing diameter. Some significant observations on the performance of footing-geogrid systems with change of the values of parametric study are presented in this paper.     

Modelling of concrete response to fluctuating load

An elastoplastic constitutive model for concrete subjected to cyclic loading conditions is presented. The model is an extension of a recently proposed constitutive concept.⁷ An initial active loading process is described, using the conventional framework of the rate independent theory of plasticity. An appropriate hardening/softening parameter is introduced which allows one to model the sensitivity of material characteristics to varying confining pressure, including a smooth transition from stable to unstable response. For stress histories that include stress reversals, the formulation invokes a set of neutral loading loci defining the conditions of the neutral state.⁸ The field of hardening moduli is specified through an appropriate interpolation rule which enables one to simulate adequately the effect of cyclic degradation of the material. The performance of the model is verified for some typical cyclic loading histories, and the results are compared with existing experimental data.     

An AI-based model for describing cyclic characteristics of granular materials

Modelling cyclic behaviour of granular soils under both drained and undrained conditions with a good performance is still a challenge. This study presents a new way of modelling the cyclic behaviour of granular materials using deep learning. To capture the continuous cyclic behaviour in time dimension, the long short-term memory (LSTM) neural network is adopted, which is characterised by the prediction of sequential data, meaning that it provides a novel means of predicting the continuous behaviour of soils under various loading paths. Synthetic datasets of cyclic loading under drained and undrained conditions generated by an advanced soil constitutive model are first employed to explore an appropriate framework for the LSTM-based model. Then the LSTM-based model is used to estimate the cyclic behaviour of real sands, ie, the Toyoura sand under the undrained condition and the Fontainebleau sand under both undrained and drained conditions. The estimates are compared with actual experimental results, which indicates that the LSTM-based model can simultaneously simulate the cyclic behaviour of sand under both drained and undrained conditions, ie, (a) the cyclic mobility mechanism, the degradation of effective stress and large deformation under the undrained condition, and (b) shear strain accumulation and densification under the drained condition.     

An anisotropic hardening model for soils and its application to cyclic loading

An anisotropic hardening model for soils is proposed by applying the concept of a field of hardening moduli developed previously for metals. Besides the yield surface, a set of nesting surfaces in the stress-space specifies the variation of hardening moduli during the deformation process. Both drained and undrained soil behaviour can be treated and distortional as well as volumetric strain cycles can be considered. The model can be applied in studying soil behaviour under cyclic loading and in particular to describe densification or liquefaction phenomena.     

低频循环荷载下地基一维固结性状分析

给出了低频梯形循环荷载下单层地基一维固结解。对该循环荷载下地基固结特性、相应的影响因素以及平均固结度、有效应力随荷载的发展和变化规律进行了分析和讨论,并研究了有效应力最大和最小值随荷载的变化规律。在任一周期中,有效应力 的发展并不与荷载的变化同步,而是按一定规律滞后发展。     

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。     

Soil–structure cyclic direct shear tests: a new interpretation of the direct shear experiment and its application to a series of cyclic tests

This paper presents a series of cyclic 2D direct shear tests on sand–rough material interfaces under constant normal load (CNL) and constant normal stiffness (CNS) conditions. The aim of these tests is to describe the behavior of the soil–pile contact subjected to a large number of cycles due to environmental or anthropic loadings. These cycles (typically 10⁴ or less due to an early rupture) are small (10, 20 and 40 kPa in terms of shear stress). A new interpretation of the direct shear tests is proposed. The sample of soil is schematically composed of a sheared interface and of a buffer under oedometric load. The problem of sand leakage between the shear box and the rough plate, classical phenomenon in this type of test, is focused. The effect of initial density, position of “center of cycles” in stress plane (mean cyclic variables) and cyclic amplitude is investigated. The cycles are defined by the initial mean cyclic normal stress, the level of initial mean cyclic stress ratio and the normalized cyclic amplitude. Under CNL condition, either dilation or contraction is exhibited, in agreement with the characteristic state developed by Luong (International symposium on soils under cyclic and transient loading, Swansea, 7–11 January, pp 315–324, 1980). The influence of a prescribed normal stiffness is especially considered. It can be highlighted that CNS cyclic paths are always contractive. This contraction results in a drop of mean cyclic normal stress often called degradation of friction.