A constitutive model for sand with anisotropic hardening rule

An anisotropic hardening model for sand or other granular materials is presented. The state of initial densification is represented by a configuration surface and the state of loading by a loading surface in the stress space. The domain of elastic response may not exist and the irreversible strain is assumed to occur for both active and reverse loading. The derived constitutive equations are applicable both for dense and loose sands. Some model predictions are compared with available experimental data for triaxial compression and extension under undrained condition.     

Numerical modeling of changes in anisotropy during liquefaction using a generalized constitutive model

A constitutive model with rotation hardening was generalized from the triaxial compression state to a general stress state. With the generalized model, numerical simulations of cyclic and monotonic undrained triaxial tests were conducted to reproduce the phenomenon of continuous, orderly and rapid changes in anisotropy during liquefaction. The simulated results demonstrated that when sand enters the liquefaction stage, the yield surface in the stress space rotates quickly, causing continuous and rapid changes in anisotropy. Through comparison of the simulated and experimental results, the generalized constitutive model was shown to be able to capture the fundamental behaviors of sand demonstrated by the experimental data, and the rotational hardening rule adopted in the generalized model was proven suitable for describing the continuous, orderly and rapid changes in anisotropy that occur during liquefaction.     

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。     

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.     

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.     

Numerical modeling of vertical drains with advanced constitutive models

The water flow into a vertical drain under an embankment loading is axisymmetric problem and therefore, the vertical drain system must be converted into equivalent plane strain model. The matching is achieved by manipulating the drain spacing and/or soil permeability according to relatively simple rules. This paper investigates the verification of matching approaches by comparing 2D plane strain and 3D unit cell results when complex constitutive models are used in the finite element analyses. The numerical results showed that the match was found to be satisfactory but not perfect. A full-scale plane strain analysis is subsequently applied to an embankment case history taken from Haarajoki, Finland, stabilized vertical drains and compared with field measurements.     

Characterization and constitutive modeling of red clay contaminated with ammonium carbonate

Conventionally, red clay is used for agricultural purposes in southern China. Fertilizers, especially urea, are commonly introduced into the red clay to improve the crop yields. However, due to the rapid urbanization in China, large areas of lands with red clays have been converted into sites for domestic and industrial constructions. Nevertheless, few researchers focused on the effect of urea on the strength and compressibility of red clay. In this research, the shear strength and compressibility of the red clay saturated by different concentrations of the (NH₄)₂CO₃ solution (urea's hydrolysates) were experimentally investigated using direct shear as well as oedometer tests, respectively. It was noticed that both the shear strength and stiffness of the red clay significantly decreased after exposure to the urea solution. In addition, the micromechanisms of the strength and compressibility of the red clay treated by the (NH₄)₂CO₃ were studied by the scanning electron microscope test and X-ray diffraction test. Based on the test results, a new model was developed to simulate the chemomechanical behavior of saturated clayey soil by modifying the Barcelona basic model (BBM) for unsaturated soils. The proposed model introduces four additional parameters, compared to the BBM, to account for the nonlinear shear strength behavior of the red clay. This model accounts for most of the complex features related to the strength and stiffness behavior of clayey soils. The parameter calibration procedures, by using the oedometer and direct shear test results, are also presented. To validate the proposed model, experimental results from the literature are considered in which illite clay samples were either mechanically or chemically or both mechanically and chemically loaded. Part of the experimental results is used to calibrate the model parameters and the other part along with the calibrated parameters is used to verify the proposed model. A comparison between experimental data and predicted results demonstrated that the proposed model is able to capture the main features related to the chemomechanical coupling behavior of saturated soils.     

Granular soils: from DEM simulation to constitutive modeling

Acta Geotechnica - In this study, the distinct element method (DEM) was employed to numerically explore the mechanical responses of granular soils and to extract key components for an elastoplastic...     

广义塑性力学的加卸载准则与土的本构模型——广义塑性力学讲座(3)

首先介绍了广义塑性力学的加卸载准则,该准则能准确判断各应变分量的加卸载状态,可以方便地应用于数值分析。然后提出了基于广义塑性力学的土本构模型。通过试验,给出了硬化压缩土和硬化剪胀土的屈服条件与计算参数,并由算例说明了其合理性。     

堆石料的剪胀特性与广义塑性本构模型

以三轴试验成果为基础,考虑颗粒破碎引起堆石料剪胀比与应力比之间的非线性关系,提出了能够反映堆石料低围压剪胀、高围压剪缩特性的剪胀方程。在广义塑性理论框架内构造堆石料的塑性流动方向向量和加载方向向量,引入依赖于密实度与平均应力的压缩参数,构造随平均应力、剪应力比和密实度变化的塑性模量,建立了一个考虑颗粒破碎的堆石料弹塑性本构模型。阐述了该模型10个参数的确定方法,并通过模拟不同围压和不同应力路径下堆石料的三轴压缩试验资料验证了模型与参数的合理性。     

Single hardening constitutive model for frictional materials II. Yield critirion and plastic work contours

A review of numerous experimental data sets for frictional materials has led to a reformulation of the condition for plastic yielding in such materials. A yield function is proposed such that yield surfaces are equivalent to plastic work contours. Two parameters are required in this function. The yield surface resembles an asymmetric tear drop in the principal stress space. It includes tensile behavior of materials with effective cohesion. Work hardening and softening behavior can be simulated through the formulation of plasticity proposed herein. The capabilities of this mathematically consistent formulation are examined by comparisons with experimental data from two- and three-dimensional tests on different frictional materials.     

岩土本构模型的数学基础与广义位势理论

对于种类繁多的岩土材料的本构模型,认识其数学基础及假设以及相关的物理意义是深刻理解和正确使用它们的基础。在本文中,揭示了目前在岩土工程中现有的不同类型的本构模型的数学基础和假设及其联系;指出了其基本的问题是其中应力（应变）或者其增量是否为一有势场的梯度矢量。同时涉及到应力与应变及其增量的主轴是否相同;有势场的梯度矢量的旋度是否为零;刚度（柔度）矩阵是否对称及其秩是否为1等。还提出了广义位势理论：可以用唯一的势函数,也可以任意设立2个或者3个其梯度矢量线性无关的势函数,用它们的梯度矢量表示应力（应变）或者其增量及塑性应变增量,用简单的试验确定参数。对于具有极其复杂力学性质的岩土材料,广义位势理论为建立统一的岩土理论模型提供了基础。关 键 词：岩土本构模型;有势场;广义位势理论     

以塑性功为硬化参数的Q2原状黄土弹塑性模拟

为了研究非饱和Q2原状黄土的力学特性,通过三轴压缩试验、各向等压试验和三轴试验卸载、再加载试验获得Q2原状黄土的力学参数,并结合弹塑性力学理论,推导出Q2原状黄土的屈服函数和以塑性功为硬化参数的硬化规律,采用相关联流动规则,建立非饱和Q2原状黄土弹塑性本构模型。通过模型计算与试验实测值比较,表明该模型基本上能反映Q2原状黄土的力学特性。     

Competition mechanism between dilation and interlocking in granular soils: DEM simulation and constitutive modeling

Acta Geotechnica - Interlocking refers to a kind of resistance caused by the staggered arrangement of granular materials. In geotechnical engineering, it is considered as one of the important...     

平面应变状态下土体的软化特性与本构模拟

在平面应变状态下,由于土体在应力峰值状态出现了应变局部化现象,从而变形模式失去了原有的均匀性而呈现软化特性。为此,采用常规的弹塑性本构模型模拟土体峰值前的均匀变形,对应力峰值状态则采用非共轴的分叉理论进行预测,而土样在峰值后出现不均匀变形的宏观力学特性则通过复合体理论加以描述。理论预测表明,构建这样的软化本构模型能真实反映平面应变状态下的应力-应变特性。理论分析还表明,经典的变形分叉理论中引入非共轴弹塑性模型,才能准确地预测土体的应力峰值,这是构建平面应变状态下土体软化本构模型的关键所在。     

Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment

Through a first-generation computational mechanics avatar that directly links advanced X-ray computed tomographic experimental techniques to a discrete computational model, we present a case study where we made the first attempt to characterize and model the grain-scale response inside the shear band of a real specimen of Caicos ooids subjected to triaxial compression. The avatar has enabled, for the first time, the transition from faithful representation of grain morphologies in X-ray tomograms of granular media to a morphologically accurate discrete computational model. Grain-scale information is extracted and upscaled into a continuum finite element model through a hierarchical multiscale scheme, and the onset and evolution of a persistent shear band is modeled, showing excellent quantitative agreement with experiment in terms of both grain-scale and continuum responses in the post-bifurcation regime. More importantly, consistency in results across characterization, discrete analysis and continuum response from multiscale calculations are found, achieving the first and long sought-after quantitative breakthrough in grain-scale analysis of real granular materials.     

Effective skeleton stress and void ratio for constitutive modeling of fiber-reinforced sand

Acta Geotechnica - Inclusion of flexible fibers such as polypropylene and polyester is an effective method for soil improvement, as it significantly enhances the soil strength and ductility. A...     

Diffuse instability of granular material under various drainage conditions: discrete element simulation and constitutive modeling

Acta Geotechnica - Diffuse instability is a typical failure mode of sand that occurs before the perfect plastic flow condition is attained. Whereas extensive laboratory experiments have...     

考虑体积变化影响的岩石应变软硬化损伤本构模型及参数确定方法

针对现有岩石损伤模型的局限性与不足,将应力作用下的岩石抽象为空隙、损伤与未损伤材料三部分,以空隙率反映岩石体积或空隙的变化,以损伤变量或损伤因子反映岩石力学性态的改变程度,通过对各部分材料的微观受力及其与宏观应力和应变的关系进行分析,建立了可反映岩石变形过程中体积或空隙变化特性的新型岩石损伤模型;从岩石微元强度合理度量方法研究入手,引进统计损伤理论,建立了可考虑损伤阀值影响的岩石统计损伤演化模型,进而建立了能模拟应变软硬化全过程的岩石统计损伤本构模型,并提出了参数确定方法。该模型不仅能反映岩石应变软硬化特性,而且能反映岩石变形的初期压密和后期扩容的特性。通过实例分析与讨论,表明模型合理与可行。