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。     

Genealogy of hypoplasticity and barodesy

This article is an attempt at providing an insight into the development of hypoplasticity (including barodesy, which is a recent development of hypoplasticity) as a theory elaborated since 1977, when the first version was published by the first author, until present. The multiplicity of the many versions published since then is hard to overlook. This article presents a review and insight into the evolution of a theory and the struggle to formulate a satisfactory constitutive law. Among the many proposed versions, we focus on those ones that can be seen as changes of paradigm. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling the viscous behavior of frozen soil with hypoplasticity

This paper presents a hypoplastic constitutive model for the viscous behavior of frozen soil. The model is composed of a ‘solid’ part and a ‘fluid’ part. The solid part is based on the extended hypoplastic model, and the fluid part is dependent on the second time derivative of strain. The performance of the model is demonstrated by simulating some uniaxial compression tests at different strain rates. Moreover, the model can describe in a unified way the three stages of typical creep tests, that is, primary, secondary, and tertiary stage. Copyright © 2016 John Wiley & Sons, Ltd.     

A comparative study of the hypoplasticity and the fabric‐dependent dilatant double shearing models for granular materials

In this paper, we consider the mechanical response of granular materials and compare the predictions of a hypoplastic model with that of a recently developed dilatant double shearing model which includes the effects of fabric. We implement the constitutive relations of the dilatant double shearing model and the hypoplastic model in the finite element program ABACUS/Explicit and compare their predictions in the triaxial compression and cyclic shear loading tests. Although the origins and the constitutive relations of the double shearing model and the hypoplastic model are quite different, we find that both models are capable of capturing typical behaviours of granular materials. This is significant because while hypoplasticity is phenomenological in nature, the double shearing model is based on a kinematic hypothesis and microstructural considerations, and can easily be calibrated through standard tests. Copyright © 2006 John Wiley & Sons, Ltd.     

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 hypoplastic constitutive model for clays

This paper presents a new constitutive model for clays. The model is developed on the basis of generalized hypoplasticity principles, which are combined with traditional critical state soil mechanics. The positions of the isotropic normal compression line and the critical state line correspond to the Modified Cam clay model, the Matsuoka–Nakai failure surface is taken as the limit stress criterion and the non‐linear behaviour of soils with different overconsolidation ratios is governed by the generalized hypoplastic formulation. The model requires five constitutive parameters, which correspond to the parameters of the Modified Cam clay model and are simple to calibrate on the basis of standard laboratory experiments. This makes the model particularly suitable for practical applications. The basic model may be simply enhanced by the intergranular strain concept, which allows reproducing the behaviour at very small strains. The model is evaluated on the basis of high quality laboratory experiments on reconstituted London clay. Contrary to a reference hypoplastic relation, the proposed model may be applied to highly overconsolidated clays. Improvement of predictions in the small strain range at different stress levels is also demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.     

Theoretical investigation of the cavity expansion problem based on a hypoplasticity model

The problem of the symmetric quasi‐static large‐strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so‐called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

一种改进的粘土亚塑性本构模型

简要地介绍了Herle和Kolymbas针对黏土建立的亚塑性本构模型的方法。结合黏土的特性以及对响应包络线的分析,详细地列出了HK模型几个尚未解决的问题,并对该模型3个参数分别进行了改进,建立了改进后的HK亚塑性公式以及参数的确定方法。改进后的模型继承了HK模型参数少、易确定以及公式简洁等特点,使HK模型不仅具有严密的数学和力学基础,而且具有较好的实际意义。     

The critical state behaviour of barodesy compared with the Matsuoka–Nakai failure criterion

Barodesy is a new approach to constitutive modelling of soil. It is based on Goldscheider's principles and maps stretching directions onto corresponding stress directions with the help of a simple exponential function. This mapping also determines a critical state surface in principal stress space. The article investigates this surface and relates it to the well‐known Matsuoka–Nakai failure criterion. It turns out that the difference between these two surfaces is negligible for practical applications. Copyright © 2011 John Wiley & Sons, Ltd.     

A hypoplastic macroelement formulation for single batter piles in sand

Batter piles are widely used in geotechnical engineering when substantial lateral resistance is needed or to avoid the interference with existing underground constructions. Nevertheless, there is a lack of fast numerical tools for nonlinear soil‐structure interactions problems for this type of foundation. A novel hypoplastic macroelement is proposed, able to reproduce the nonlinear response of a single batter pile in sand under monotonic and cyclic static loadings. The behavior of batter piles (15°, 30°, and 45°) is first numerically investigated using 3D finite element modeling and compared with the behavior of vertical piles. It is shown that their response mainly depends on the pile inclination and the loading direction. Then, starting from the macroelement for single vertical piles in sand by Li et al (Acta Geotechnica, 11(2):373‐390, 2016), an extension is proposed to take into account the pile inclination introducing simple analytical equations in the expression describing the failure surface. 3D finite element numerical models are adopted to validate the macroelement that is proven able to reproduce the nonlinear behavior in terms of global quantities (forces‐displacements) and to significantly reduce the necessary computational time.     

Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during quasi‐static shearing of an infinite layer under plane strain conditions, free dilatancy and constant pressure. For a simulation of the mechanical behaviour of a cohesionless granular material during a monotonous deformation path, a micro‐polar hypoplastic constitutive relation was used which takes into account particle rotations, curvatures, non‐symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. In the paper, a deterministic and statistical size effect is analysed. The deterministic calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2000 mm. To investigate the statistical size effect, the Monte Carlo method was applied. The random distribution of the initial void ratio was assumed to be spatially correlated. Truncated Gaussian random fields were generated in a granular layer using an original conditional rejection method. The sufficient number of samples was determined by analysing the convergence of the outcomes. In order to reduce the number of realizations without losing the accuracy of the calculations, stratified and Latin hypercube methods were applied. A parametric analysis of these methods was also presented. Some general conclusions were formulated. Copyright © 2007 John Wiley & Sons, Ltd.     

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

A thermo‐mechanical model for variably saturated soils based on hypoplasticity

The paper presents a mechanical model for non‐isothermal behaviour of unsaturated soils. The model is based on an incrementally non‐linear hypoplastic model for saturated clays and can therefore tackle the non‐linear behaviour of overconsolidated soils. A hypoplastic model for non‐isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step‐by‐step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo‐mechanical behaviour of an unsaturated compacted silt. Copyright © 2011 John Wiley & Sons, Ltd.     

FE-studies on the influence of initial void ratio,pressure level and mean grain diameter on shear localization

The paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The influence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a finite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FE-calculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar effects manifested by the appearance of grain rotations and couple stresses are only significant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement. Copyright © 1999 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 general approach to model interfaces using existing soil constitutive models application to hypoplasticity

The modelling of interfaces is important for the holistic simulation of geotechnical structures (e.g. piles, tunnels and geogrids). For this reason, advanced constitutive interface models and numerical techniques are needed. There are few user-friendly models, and these are rarely implemented. In this paper, a new approach for advanced interface models is proposed. This is based on the assumption that the fully rough interface can be modelled considering simple-shear behaviour at the interface. A 3D soil model is used as a constitutive driver for a frictional subroutine. This minimises the effort required, and advanced interface models are available with less effort. Two different hypoplastic models are used with the new approach. The approach was verified for several aspects (e.g. mesh size dependence), and the volumetric behaviour was studied. The user-friendliness and absence of additional parameters led to more realistic simulation results. The proposed method can be extended to other modelling techniques and will improve the modelling of contacts in soil-structure interaction analysis.