Observations on the extended Matsuoka–Nakai failure criterion

The equivalent Mohr–Coulomb (M‐C) friction angle ? (J. Geotech. Eng. 1990; 116 (6):986–999) of the extended Matsuoka–Nakai (E‐M‐N) criterion has been examined under all possible stress paths. It is shown that ? depends only on the ratio of cohesion to confining stress c^′/σ and the frictional angle ?, where ? is the friction angle measured in triaxial compression (or extension) to which the E‐M‐N surface is fitted. It is also shown that ? is independent of c^′, when σ=0 and of σ when c^′=0, with the former representing an upper bound and the latter a lower bound of ? for any particular stress path. The closest point projection method has also been implemented successfully with the E‐M‐N criterion, and plane strain and axisymmetric element tests performed to verify some theoretical predictions relating to failure and post‐yielding behavior. Finally, a bearing capacity problem was analyzed using both E‐M‐N and M‐C, highlighting the conservative nature of M‐C for different friction angles. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑物态变化的粗粒土亚塑性本构模型

建立了可描述粗粒土单调和循环力学特性的一个亚塑性本构模型。基于亚塑性理论的基本框架,引入临界状态参数,建立了一个新的粗粒土亚塑性模型,给出了数学公式及参数确定方法。采用该模型对粗粒土单调和循环加载试验进行了模拟和预测。该模型无需判断加卸载、参数较少、易于三维化,能够较全面地描述单调和循环荷载作用下粗粒土的主要力学特性,如强度与围压的非线性关系,胀缩规律与围压相关、卸载体缩、体变随加载过程累积等主要体变特性等。     

A fully convex reformulation of the original Matsuoka–Nakai failure criterion and its implicit numerically efficient integration algorithm

This paper presents a reformulation of the original Matsuoka–Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non‐associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd.     

A hypoplastic model for granular soils incorporating anisotropic critical state theory

It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress-strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus-Bauer hypoplastic model, and a scalar-valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.     

Modelling the time‐dependent behaviour of granular material with hypoplasticity

This paper presents a constitutive model for time‐dependent behaviour of granular material. The model consists of 2 parts representing the inviscid and viscous behaviour of granular materials. The inviscid part is a rate‐independent hypoplastic constitutive model. The viscous part is represented by a rheological model, which contains a high‐order term denoting the strain acceleration. The proposed model is validated by simulating some element tests on granular soils. Our model is able to model not only the non‐isotach behaviour but also the 3 creep stages, namely, primary, secondary, and tertiary creep, in a unified way.     

亚塑性理论简介

简要介绍了亚塑性理论和亚塑性本构模型以及在颗粒材料力学分析上的应用。详细地介绍了亚塑性模型参数的确定方法。亚塑性本构模型不是从弹塑性理论发展而来,它是以非线性张量为基础,没有屈服面、塑性势、流动法则、硬化定律以及把变形分解为弹性和塑性部分等概念。亚塑性在很多方面具有一定的优越性,特别是涉及到应力水平非常低或者非常高的情况。     

An SMP critical state model for methane hydrate‐bearing sands

Mechanical properties of methane hydrate‐bearing soils are complex. Their behavior undergoes a significant change when hydrates dissociate and become methane gas. On the other hand, methane hydrates are ice‐like compounds and, depending on the hydrate accumulation habits and the degree of hydrate saturation, may cement soil particles into stronger and stiffer soils. A new constitutive model is proposed that is capable of capturing essential characteristics of hydrate‐bearing soils. The core of the model includes the spatial mobilized plane concept; a transformed stress, t_ij; the critical state; and the subloading framework. The proposed model gives soil responses due to stress changes or hydrate saturation changes or both. The performance of the model has been found satisfactory, over a range of hydrate saturation and confining pressures, using triaxial test data from laboratory‐synthesized samples and from field samples extracted from Nankai Trough, Japan. Copyright © 2015 John Wiley & Sons, Ltd.     

Non‐uniqueness of critical state line in compression and extension conditions

Experimental evidence has indicated that the critical state line determined from undrained compression tests is not identical to that determined from undrained extension tests. The purpose of this paper is to investigate a modelling method that accounts for the non‐uniqueness of critical state lines in the compression and the extension testing conditions. Conventional elastic–plastic cap models can predict only a unique critical state line for the compression and the extension tests. A new micromechanical stress–strain model is developed considering explicitly the location of critical state line. The model is then used to simulate undrained triaxial compression and extension tests performed on isotropically consolidated samples with different over‐consolidated ratios. The predictions are compared with experimental results as well as that predicted by models with kinematic hardening of yield surface. All simulations demonstrate that the proposed micromechanical approach is capable of modelling the undrained compression and the undrained extension tests. Copyright © 2009 John Wiley & Sons, Ltd.     

A single numerically efficient equation for approximating the Mohr–Coulomb and the Matsuoka–Nakai failure criteria with rounded edges and apex

This paper presents a novel formulation for defining soil failure. It plots in the principal stress space as a surface with the shape ranging between an approximation of the Matsuoka–Nakai and of the Mohr–Coulomb criteria depending on the value of a single parameter. The new function can be used as a replacement of the original equations of these well‐established criteria for implementing in a program for numerical analyses, and it is particularly effective for approximating the Matsuoka–Nakai criterion. Both the Mohr–Coulomb and the Matsuoka–Nakai failure criteria present numerical difficulties during implementation and also at run‐time. In the case of the Matsuoka–Nakai, the new formulation plots in the first octant only, whereas the original criterion plots in all octants, which causes severe convergence problems particularly for those Gauss points with low stress state, such as those on the side of a shallow footing. When the shape parameter is set to reproduce the Mohr–Coulomb failure criterion, on the other hand, the new formulation plots as a pyramid with rounded edges. Moreover, as the new function is at least of class C², the second derivatives are continuous, thus ensuring quadratic convergence of the Newton's method used within the integration scheme of the constitutive law. The proposed formulation can also provide both sharp and rounded apex of the surface at the origin of the stress space by setting accordingly one additional parameter. Copyright © 2013 John Wiley & Sons, Ltd.     

Exploring the influence of interparticle friction on critical state behaviour using DEM

Understanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.     

A critical state sand plasticity model accounting for fabric evolution

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.     

CASM: a unified state parameter model for clay and sand

The purpose of this paper is to present a simple, unified critical state constitutive model for both clay and sand. The model, called CASM (Clay And Sand Model), is formulated in terms of the state parameter that is defined as the vertical distance between current state (v, p′) and the critical state line in v–ln p′ space. The paper first shows that the standard Cam-clay models (i.e. the original and modified Cam-clay models) can be reformulated in terms of the state parameter. Although the standard Cam-clay models prove to be successful in modelling normally consolidated clays, it is well known that they cannot predict many important features of the behavior of sands and overconsolidated clays. By adopting a general stress ratio-state parameter relation to describe the state boundary surface of soils, it is shown that a simple, unified constitutive model (CASM) can be developed for both clay and sand. It is also demonstrated that the standard Cam-clay yield surfaces can be either recovered or approximated as special cases of the yield locus assumed in CASM. The main feature of the proposed model is that a single set of yield and plastic potential functions has been used to model the behaviour of clay and sand under both drained and undrained loading conditions. In addition, it is shown that the behaviour of overconsolidated clays can also be satisfactorily modelled. Simplicity is a major advantage of the present state parameter model, as only two new material constants need to be introduced when compared with the standard Cam-clay models. © 1998 John Wiley & Sons, Ltd.     

基于数据融合的边坡临滑状态确定方法

安全监测及数值模拟是评估边坡稳定性状态的两种重要手段,但是,如何根据监测信息及数值模拟成果确定边坡的临界失稳状态一直是边坡工程领域关注的重点问题。首先基于层次聚类方法计算边坡不同类型状态变量监测点的欧式距离,根据距离大小筛选出边坡的有效监测点;然后,计算同种类型状态变量有效监测点的熵权值,采用熵权融合方法对有效监测点进行数据层融合,得到不同类型状态变量对应的融合监测指标曲线;其次,采用主成分分析法对多种数据层融合监测指标曲线进行特征层融合,得到可反映全部状态变量信息特征的综合监测信息曲线,进而构建了边坡渐进失稳过程中不同监测变量的信息挖掘融合框架;最后,提出了一种缓变曲线的变点搜索方法,采用该方法对综合监测信息曲线开展变点分析,搜索边坡状态渐进演化的突变点（即边坡临滑状态点）。将所提出的方法应用到某公路边坡临界失稳状态的确定中,结果表明,单个监测点或单个融合指标的累积值、变化速率作为边坡失稳判据存在不唯一性,融合多种监测数据建立的综合监测信息序列可以较好地反映边坡状态演化特征,可避免单一状态变量的单一监测点数据对边坡状态的误判,验证了所提方法的可行性和适用性。     

一类新型的散粒型土体本构理论

详细地介绍了国际上近30才发展起来的具有独特建模思想的一类新型的散粒型土体本构建模理论--亚塑性本构理论。将该理论与经典的弹塑性理论进行比较后发现,亚塑性理论的本构表达式自动隐含了弹塑性理论中相对应的一些基本概念和假定,无需额外引入,因此增加了模型的客观性。以Gudehus-Bauer亚塑性模型为例,分析了模型在临界状态时的本构特征。此外,通过三轴试验和循环剪切试验的亚塑性数值模拟表明,亚塑性本构模型能很好地反映无黏性散粒型土体的非弹性、非线性及剪胀（剪缩）性等主要应力-应变特性。     

Mohr–Coulomb MiniCLoE model Uniqueness and localization studies,links with normality rule

This paper is devoted to a parametric study of a plane Mohr–Coulomb CLoE model. As CLoE models are designed with a consistency condition, it is possible to define a normality condition and to study its consequences. The positiveness of the second order work which implies the uniqueness of the solution of a small strain boundary value problem is studied firstly. Then the localization criterion is also studied. It is proved that normality has consequences similar to those for classical elasto plastic models. However if induced anisotropy is introduced in the hypoplastic CLoE model, some conclusions are no longer true. Finally plane strain experimental data are used to identify the parameters of the model. Copyright © 2002 John Wiley & Sons, Ltd.     

A micro‐mechanical study of peak strength and critical state

We present a micro‐mechanical analysis of macroscopic peak strength, critical state, and residual strength in two‐dimensional non‐cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain‐scale counterparts (e.g., inter‐particle contact forces, fabric, particle displacements, and velocities), providing an across‐the‐scale basis for a better understanding and modeling of granular materials. These multi‐scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain‐scale mechanics are established. Second, these relations are used in conjunction with the non‐associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro‐mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro‐mechanical conditions for peak strength, critical state, and residual strength. Copyright © 2015 John Wiley & Sons, Ltd.     

结构性黄土临界状态力学性状

土颗粒之间的联结方式和排列方式是影响土的结构性的两个主要因素,而水和外力可以改变土颗粒间的联结方式和排列方式,破坏了土的结构性。当排列是影响黄土结构性的主要因素时,在外力的作用下,K0结构性黄土表现出临界状态力学性状。对饱和K0结构性黄土进行不同试验,应用临界状态土力学理论进行归纳,分析其规律,总结出在外力作用过程中K0结构性黄土的结构性特殊物理力学性质,为建立结构性土的本构模型提供有力的试验依据。     

基于热力学的临界状态模型的返回映射算法及实现

相对于其他临界状态模型,基于热力学的临界状态（TCS）模型不需要引入塑性势假设,能够自动满足热力学定律。通过对TCS的修正,使其能够模拟初始K0固结的影响,利用了返回映射算法进行了TCS模型的ABAQUS本构二次开发,通过与ABAQUS内嵌的修正剑桥模型（MCC）计算结果的对比,证实了该程序的可靠性。对模型中的2个控制屈服面形状的参数进行了讨论,分析了它们对应力-应变关系与剪胀关系的影响,修改TCS模型参数可以实现非椭圆的屈服面,进而拓展了模型的适用范围,不同的参数对于屈服面形状和大小的影响也有所不同。同时还比较了采用考虑K0固结及旋转硬化的TCS模型与不考虑K0固结及旋转硬化的MCC模型所得到的应力-应变关系与剪胀关系的差异。对于真实土体,K0固结及旋转硬化是土体的基本力学特性。最后证明了TCS模型较MCC模型（模型中没有考虑旋转硬化与K0固结对硬化规律的影响）可以很好地模拟该特性,所以更加有效。     

Modelling the poroelastoplastic behaviour of soils subjected to internal erosion by suffusion

Granular soils subjected to seepage flow may suffer suffusion, ie, a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius-Duhem inequality accounting for dissipation due to suffusion, and we deduce restrictions on the constitutive laws of the soil. We suggest (a) a possible coupling between the seepage forces and the suffusion kinetics and (b) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains and the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided.     

边坡稳定临界破坏状态的动力学评判方法

针对目前用有限单元法分析边坡稳定时,对临界状态判别存在的一些问题和不足,提出了边坡稳定临界破坏状态的动力学评判方法。该方法以加速度是否为零作为边坡是否稳定的判据,同静力方法相比,具有物理意义明确,计算易收敛等优点。在分析滑动本质的基础上,提出通过搜索剪应变最大的点以确定临界滑裂面的方法。算例证明了临界状态动力学评判方法的可靠性。