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1.
This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials. 相似文献
2.
Soil is a heterogeneous material and most natural soil deposits show a definite stratification. The mechanical behaviour of such material is generally different in different directions, especially in the direction parallel and perpendicular to the stratification. A series of isotropic compression tests were carried out to study the behavior of granular material produced under controlled stratification in the laboratory. These tests were conducted both on cylindrical and square prismatic tri-axial specimens. It was observed that for hydrostatic loading, the strain response was different in different directions, especially in directions parallel and perpendicular to the direction of soil deposition. A definite trend of anisotropy was observed in the deformation pattern. The observed anisotropy is modeled in this paper by treating soil-dilatancy as a variable quantity. The equation of the plastic potential surface of the model which obeys a non-associated flow rule, is assumed to be dependent on three main variables confining pressure ( \(\sigma_{3}\)), void ratio (e) and the angle of bedding plane orientation (δ) during deposition. The angle of bedding plane orientation (δ) was measured with respect to the direction of the major principal stress. The model has a cap yield surface in the isotropic stress direction, which is supplemented by a shear hardening Mohr–Coulomb surface in the deviator direction. This paper focuses on predicting the anisotropic strain response of stratified soil deposits subjected to isotropic compression. The proposed anisotropic model incorporates within an existing strain-hardening sand model, a modified cap yield surface and a modified plastic potential function related to the cap surface, to account for the anistropic response observed in isotropic compression tests. The two dimensional stress–strain model was extended to three dimensional Cartesian space. The strain anisotropy observed in the isotropic compression tests was predicted by the three dimensional anisotropic model proposed for granular materials. 相似文献
3.
Granular materials like sand are widely used in civil engineering. They are composed of different sizes of grains, which generate a complex behaviour, difficult to assess experimentally. Internal instability of a granular material is its inability to prevent the loss of its fine particles under flow effect. It is geometrically possible if the fine particles can migrate through the pores of the coarse soil matrix and results in a change in its mechanical properties. This paper uses the three‐dimensional Particle Flow Code (PFC3D/DEM) to study the stability/instability of granular materials and their mechanical behaviour after suffusion. Stability properties of widely graded materials are analysed by simulating the transport of smaller particles through the constrictions formed by the coarse particles under the effect of a downward flow with uniform pressure gradient. A sample made by an initially stable material according to the Kenney & Lau geometrical criterion was divided into five equal layers. The classification of these layers by this criterion before and after the test shows that even stable granular materials can lose fine particles and present local instability. The failure criterion of eroded samples, in which erosion is simulated by progressive removal of fine particles, evolves in an unexpected way. Internal friction angle increases with the initial porosity, the rate of lost fine particles and the average diameter D50. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
The stress solution in plasticity with an associated or a non-associated flow rule is considered. Upon fully implicit integration of the relevant constitutive relations the stress is obtained as the projection of the (fictitious) elastic stress onto the yield surface for given values of the hardening softening variables. This projection is defined, for a general non-associated flow rule, in adjusted complementary elastic energy, which becomes exactly the complementary energy when the flow rule is associated. Isotropic elasticity and mean-stress dependent isotropic yield criteria (pertinent to soil) are considered and the implications of a certain class of non-associated flow rules are evaluated. This class relates to dilatant (or contractant) materials and involves non-associated plastic volume change. The corresponding stress solutions are shown to be strongly influenced by Poisson's ratio and by the dilation angle. 相似文献
5.
粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。 相似文献
6.
This paper is concerned with a fundamental assumption in the theory of plasticity: the direction of plastic strain increments is independent of the loading (stress) increment direction. This assumption, also known as plastic flow rule postulate, works quite well for metal‐like materials. However, geomaterials such as sand present deformational mechanisms that are distinctive from those of metals when they are loaded. As such, we hereby examine the validity of this postulate for granular media accounting for their discrete nature. This is accomplished by analysing the mechanical behaviour of a cubic assembly of polydispersed spherical articles using a particle flow code. An extension to Gudehus' response envelope to three‐dimensional conditions is used to study the incremental character and influence of loading direction on the behaviour of these materials. It is found that plastic flow in granular media is governed by both current state variables and incremental loading direction and magnitude, especially under non‐axisymmetric stress conditions. The flow rule postulate of plasticity remains valid only in axisymmetric and biaxial conditions. We also verified that the plastic response might be significantly influenced by the stress path (or history) taken prior to loading. These findings raise the question of whether or not classic elastoplastic models based on the above postulate will have serious shortcomings, especially in true‐triaxial conditions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
7.
A severe dependence of numerical simulations on the mesh density is usually attributed to the presence of strain softening in the constitutive relation. However, other material instabilities, like non-associated plastic flow, can also cause mesh sensitivity. Indeed, loss of ellipticity in quasi-static analyses is the fundamental cause of the observed mesh dependence. It has been known since long that non-associated plastic flow can cause loss of ellipticity, but the consequence for mesh sensitivity, and subsequently, for the difficulty of the equilibrium-finding iterative procedure to converge have remained largely unnoticed. We first demonstrate at the hand of a biaxial test structural softening and a marked mesh dependence for an ideally plastic material equipped with a non-associated flow rule. The phenomena are then analysed in depth using an infinitely long shear layer. Finally, it is shown that the mesh effect disappears when the standard continuum model is replaced by a Cosserat continuum, a well-known regularisation method for strain-softening constitutive relations. 相似文献
8.
The unified three-dimensional (3D) critical state bounding-surface plasticity model gUTS enables clays, silts and sands to be treated within a single framework. Furthermore, loose and dense states of a particular soil subjected to a wide range of confinements are viewed as a single material defined by the same set of constants. The model is able to handle both monotonic and complex cyclic paths including those involving a rotation of the principal stress directions. The model incorporates the following features: combined use of radial and deviatoric mapping rules and the use of an apparent normal consolidation line for sands; use of a non-associated flow rule where the ratio of the rates of volumetric plastic strain to deviatoric plastic strain is a function only of the ratio of deviatoric to mean effective stresses and the Lode angle; adoption of a bi-linear critical state line projected onto the plane of the void ratio versus logarithm of mean effective stress; inclusion of a sub-elliptic, or super-elliptic, segment in the plastic dilatancy surface for stress ratios less than critical; use of elliptic segments in the deviatoric planes; movement of the projection centre in the deviatoric mapping region and incorporation of a plastic stiffening effect for cyclic paths which repeatedly load in the same deviatoric direction. 相似文献
9.
土体在剪切变形过程中产生主应力方向的旋转时,主应变增量方向与主应力方向之间存在着非共轴现象,然而传统的弹塑性本构模型未能考虑该现象的影响。通过在屈服面的切线方向增加一项非共轴塑性应变增量,即可实现对非共轴现象的反映。采用显式积分算法和自动分步方法,将非共轴本构模型运用到桶形基础地基承载力问题的有限元计算中,并讨论了流动法则、内摩擦角、膨胀角等因素与非共轴模型的联系。计算结果表明：采用有限元程序默认容许误差时,该本构模型可达到理想的收敛精度,并且,该模型对关联、非关联流动法则均适用。采用共轴模型进行数值计算时,不同流动法则对计算结果的影响可以忽略;采用非共轴模型时,不同流动法则的计算结果之间存在差异。非共轴现象对地基承载力-位移曲线具有软化作用,并且,该软化作用在采用非关联流动法则时变得更加明显 相似文献
10.
岩土材料属于摩擦型材料,其强度特性时参数指标的选取至关重要。当前对剪胀角存在模糊认识,导致在理论分析和数值模拟分析中常会产生较大误差。在分析传统的滑移线场理论的基础上,采用广义塑性理论,证明了岩土材料在非关联流动法则条件下的剪胀角应取? /2,且此时体变必为0。通过对具有精确理论解的经典Prandtl地基承载力课题的数值模拟分析,分别对关联流动法则、非关联流动法则剪胀角取? /2及非关联流动法则剪胀角取0三种情况下地基的承载力进行了计算。结果表明,上述3种情况下得到的极限荷载的误差为2 %,但滑移线场与理论解有较大差异。其中,在非关联流动法则条件下,采用剪胀角? =? /2所得到的滑移线场与Prandtl理论解一致,而采用? =0所得到的滑移线场与理论解有较大的偏差。这说明目前在非关联流动法则条件下采用? = 0虽然可得到相应的正确的极限荷载,但是相应的滑移线场具有较大的误差,同时也证明了岩土材料在非关联流动法则条件下的剪胀角应该选取? /2,而不是目前通常采用的0。 相似文献
11.
The published literature has revealed conflicting results regarding the effect of low plastic fines fraction (Ip?≤?5.0%) on the mechanical behavior of sandy soils. For this reason, the use of different sample initial structures as (initial relative density approach, global void ratio index approach, etc.) could explain these different mechanical responses of granular materials. Thus, it is necessary to evaluate the quantitative aspect of the low plastic fines effects on the undrained monotonic response of sand-silt mixtures using the global void ratio approach. To achieve this goal, an experimental testing program through controlled monotonic triaxial tests was carried out on reconstituted saturated Chlef sand containing from 0 to 50% silt with an interval of 10% at three global void ratios (e?=?0.64, 0.66 and 0.68) and subjected to constant confining pressure (σ'3?=?100 kPa). The different samples were reconstituted using two different preparation techniques: DFP and MT. The obtained results show that the low plastic fines content appears as a very relevant parameter in the characterization of the mechanical response of sand-silt mixture samples reconstituted at constant global void ratios, where the steady state shear strength and instability shear strength decreased with the increase in low plastic fines content up to the limiting fines contents (Fc?=?40% and Fc?=?10%) considering both studied initial structures (Dry funnel pluviation and Moist tamping), respectively. Beyond these thresholds fines contents, a reverse trend was observed for all parameters under study. Moreover, the test results indicate that the brittleness index, flow potential (Vf), friction index, equivalent void ratio (e*) and equivalent relative density (Dr*) could be considered as reliable parameters in the prediction of the mechanical behavior of the silty sand soils under study. 相似文献
12.
Stability and bifurcation of plane-strain, undrained, rectilinear deformations on water-saturated granular soil specimens are discussed. The soil, sand or normally consolidated clay, is described by a 2D-flow theory of plasticity for frictional material with non-associated flow rule. Contractant material become unstable (liquefies) at the state of maximum deviatoric stress. For dilatant material the dominant failure mode is shear banding that occurs close to the state of maximum principal effectivestress ratio. The theoretical findings are supported by and are used to explain existing experimental results. 相似文献
13.
由于经典的塑性力学无法根据Drucker塑性公设从理论上证明非相关联流动准则,因而从连续介质热力学基本原理出发研究土的弹塑性模型。根据率无关塑性力学理论,通过Gibbs自由能和多个独立耗散函数,建立土的多重屈服准则及其流动准则,证明了屈服准则重数和独立耗散函数个数相等,分析了耗散函数形式对屈服准则和塑性流动准则的影响。分析了一簇新的能够同时考虑相关联流动准则和非相关联流动准则的粘土的Gibbs自由能和耗散函数的表达式,殷宗泽双屈服面模型是其特例,但新模型具有更为明确的物理含义,能考虑非相关联流动准则的情况。根据粘土室内实验选取了模型参数,并与实测应力-应变曲线进行对比,说明新模型可以模拟粘土的多重屈服面本构关系。 相似文献
14.
Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
15.
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. 相似文献
16.
The behavior of granular materials is known to depend on its loose or dense nature, which in turns depends both on density and confining pressure. Many models developed in the past require the use of different sets of constitutive parameters for the same material under different confining pressures. The purpose of this paper is to extend a basic generalized plasticity model for sands proposed by Pastor, Zienkiewicz and Chan by modifying the main ingredients of the model flow—rule, loading–unloading discriminating direction and plastic modulus—to include a dependency on the state parameter. The proposed model is tested against the available experimental data on three different sands, using for each of them a single set of material parameters, finding a reasonably good agreement between experiments and predictions. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
修正剑桥模型假设体积塑性功的一半转化为耗散能,一半转化为由塑性变形约束的自由能,但通常体积耗散能和塑性体积自由能并不相等。基于热力学理论,通过引进间隔应力比来表征体积塑性功和塑性体积自由能的比例关系,构建了一个土的体积硬化模型。由于岩土材料耗散函数与所处的应力状态有关,因此,需要应用非关联流动法则,修正剑桥模型是适合应用相关联流动法则的一个特例,也是所提出模型的一个特例。 相似文献
18.
In this paper, liquefaction potential of loose sand deposit subjected to an earthquake loading is evaluated. The analysis is performed by using a finite element technique incorporating the equations of dynamics of saturated porous elastoplastic media. The soil response is modelled by an anisotropic hardening rule, similar to that as proposed by Poorooshasb and Pietruszczak. 1 The concept is based on the theory of bounding surface plasticity incorporating a non-associated flow rule and the idea of reflected plastic potential. The present paper provides a modified formulation to that discussed in Reference 1. Modifications are aimed at simplifying the concept for numerical implementations. 相似文献
19.
简要介绍了建立岩土材料弹塑性本构模型的热力学方法。它不仅具有紧凑的数学结构,而且自动满足热力学定律,仅从两个热力学势函数,即自由能函数与耗散增量函数出发,就足以导出弹塑性理论必须的屈服条件,流动法则,硬化定律和弹性定律。通过理论证明指出,只要耗散增量函数依赖于当前应力,流动法则必然是非关联的,岩土材料的摩擦特性与非关联流动法则密不可分。介绍该方法在三维模型,岩土材料的微细观力学特性,应力应变的均匀化以及剪胀和各向异性方面应用的主要研究进展,并对一些重要的概念,诸如“储存的塑性功”,“Reynolds-Taylor状态”等,进行分析与解释。最后给出近期需进一步深入研究的几点建议。 相似文献
20.
An axisymmetric lower bound limit analysis technique in combination with the finite elements has been used to investigate the effect of considering a non-associated flow rule on the stability number (γH/c) for a vertical circular unsupported excavation in a general cohesive–frictional soil medium, where (1) H is the excavation height, (2) γ defines the unit weight of the soil mass, and (3) c indicates the cohesion of the soil mass. The results are derived for different magnitudes of dilative coefficient (η), friction angle (?), and normalized excavation height (H/b), where b = the radius of the excavation. The results clearly indicate the increase in γH/c with an increase in η value. It is expected that the charts provided in this note will be quite helpful for the practicing engineers. 相似文献
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