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.     

A simple hypoplastic constitutive model for sand

The paper presents a hypoplastic constitutive model for the three-dimensional non-linear stress–strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non-linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions.     

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。     

A basic hypoplastic constitutive model for sand

Hypoplastic constitutive models are based on nonlinear tensor functions and are characterized by simple formulation and few parameters. In its early stage, mainly basic hypoplastic constitutive equations were concerned, where the stress tensor is assumed as the only state variable. There followed some enhanced models based on the basic constitutive equation by including void ratio as an additional state variable. In this paper, we first show that the widely used hypoplastic model by Wolffersdorff is seriously flawed because the underlying basic equation does not perform properly. We proceed to develop a basic hypoplastic constitutive equation by introducing a new tensorial term, which preserves the critical state at large strain. The model performance is demonstrated by parameter study for some element tests. This simple and robust basic equation is well suited to build more sophisticated models.     

堆石料Gudehus-Bauer亚塑性本构模型改进及参数确定方法

研究了Gudehus-Bauer亚塑性本构模型和模型参数的求取方法。采用侧限压缩试验曲线求取模型参数颗粒硬度hs和指数n。根据模型方程的推导,建立了拟合指数 和 与围压之间的关系,并提出了新的拟合参数。考虑到堆石料具有明显的剪胀、剪缩性,在Gudehus-Bauer模型线性项中增加了主要控制体积应变项 ,以改善模型对堆石料体积应变曲线的描述。采用堆石料大型侧限压缩试验、常规三轴试验分别验证了新的拟合参数和改进后的Gudehus-Bauer亚塑性本构模型。与堆石料试验成果比较,提出的新拟合参数与改进后的Gudehus-Bauer亚塑性本构模型可以较好地模拟堆石料的应力-应变特性,并较好地改善了堆石料体变曲线的模拟结果。对改进后的模型作了常规三轴加、卸载模拟,模拟结果反映了改进的Gudehus-Bauer亚塑性本构模型具有一定的卸载适应性。     

考虑颗粒破碎对特征孔隙比影响的堆石体亚塑性本构模型

颗粒破碎是影响堆石体强度和变形特性的主要问题之一。相比于砂土,堆石料在较低的应力水平下就会发生严重的颗粒破碎,因此,在进行堆石体力学特性及本构模型研究时必须考虑颗粒破碎的影响。同时,堆石体在受力过程中孔隙比是变化的,而传统本构模型不能使用一组参数模拟不同孔隙比的同种材料。因此,以能够考虑应力水平和土体孔隙比影响的Gudehus-Bauer亚塑性本构模型为基础,考虑堆石体有别于砂土的孔隙比变化特征,提出了考虑堆石破碎的亚塑性本构模型。亚塑性理论是目前可最大限度地减少人为假定的一种本构理论,颗粒材料在不同特征应力路径下,破碎造成的过度变形量不同;但相同应力水平、不同特征应力路径下孔隙比已不满足Gudehus-Bauer亚塑性本构模型中提出的等比例变化规律。据此,结合考虑颗粒破碎的临界状态理论和堆石体常规三轴试验和循环加载试验结果,提出了考虑颗粒破碎堆石体特征孔隙比的表达式,并将其引入到Gudehus-Bauer亚塑性本构模型中,建立了考虑颗粒破碎的堆石体亚塑性本构模型,提出了模型参数的确定方法。与堆石体试验结果对比表明,该本构模型可以较好地模拟其力学与变形特性。     

Gudehus-Bauer亚塑性本构模型研究

无黏性土的应力-应变关系可以用Gudehus-Bauer亚塑性本构模型来模拟,该模型强调应力增量的大小和方向不仅与当前应力状态有关,而且还取决于当前应变增量的大小和方向。为分析其与传统弹塑性理论的不同之处,对Gudehus-Bauer理论的线性项和非线性项进行了研究,并对不同初始孔隙比下Gudehus-Bauer亚塑性模型的应力-应变关系进行了探讨。结果表明Gudehus-Bauer亚塑性模型不用把应变分为弹性和塑性部分就能考虑不可逆变形,并能体现密砂的剪胀特性和应变软化特性以及松砂的剪缩特性和应变硬化特性。     

A fiber-reinforced constitutive model for earthen materials

Acta Geotechnica - A new elasto-plastic constitutive model for fiber-reinforced materials is developed. The model considers the effect of distributed fibers embedded in a matrix. A numerical...     

堆石料状态相关弹塑性本构模型

堆石料的强度变形特性与初始孔隙及应力状态等因素相关。建立了能够预测不同初始孔隙与初始围压影响的堆石料弹塑性本构模型。在剑桥类本构模型框架内,模型能够反映随着孔隙与围压的增大,变形特性由剪胀趋于剪缩的规律。模型采用了基于颗粒体材料细观结构变化的屈服函数和非关联流动准则,提出了能够反映堆石料正常固结线不唯一的硬化参数。为了反映状态相关性,假定堆石料存在唯一的临界状态面,探讨了考虑状态相关性需要满足的数学条件,从而对剪胀方程与硬化参数进行了修正。提出了基于粒子群优化算法的模型参数快速确定方法,将某筑坝堆石料不同初始孔隙比与围压条件下模型预测结果与三轴试验结果对比,验证了模型的合理性。     

Numerical integration and FE implementation of a hypoplastic constitutive model

Hypoplastic constitutive equation based on nonlinear tensor functions possesses a failure surface but no yield surface. In this paper, we consider the numerical integration and FE implementation of a simple hypoplastic constitutive equation. The accuracy of several integration methods, including implicit and explicit methods, is examined by performing a set of triaxial compression tests. Adaptive explicit schemes show the best performance. In addition, the stress drift away from the failure surface is corrected with a predictor-corrector scheme, which is verified by two boundary value problems, i.e. rigid footing tests and slope stability.     

A damage hypoplasticity constitutive model for cemented sand and gravel materials

Acta Geotechnica - A hypoplastic constitutive model is proposed to model the cementation-induced enhanced stiffness, strength and dilative behavior of cemented sand and gravel materials. The model...     

An enhanced constitutive model for crushable granular materials

Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state‐based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good‐quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd.     

循环荷载作用下考虑颗粒破碎的堆石体本构模型

中国西部兴建的很多200～300 m高的堆石坝处于高烈度地震区。应力水平高时堆石体的颗粒破碎对其在循环荷载作用下的应力、应变特性有重要的影响。基于广义塑性理论,通过引入状态参数,建立了循环荷载作用下考虑颗粒破碎的堆石体的本构模型,并给出了模型参数的确定方法。与堆石体在400、800、1 500、2 200 kPa围压作用时的试验结果对比,表明所提出的本构模型可以较好地模拟循环荷载作用下颗粒破碎时堆石体的动应力和动应变响应。     

Implementation of a general constitutive model for geological materials

A generalized constitutive model is described with particular attention to determination of material constants, and its implementation. The model involves use of only a single function to characterize the complete range of plastic yielding, and employs a special function to describe plastic hardening. Laboratory behaviour of an artificial soil is used to iliustrate the determination of the constants and verification of the model.     

基于黏弹塑性本构模型的泥石流数值模拟

泥石流是一个世界范围的地质灾害问题,多年来受到广泛而深入的研究。大多数工作致力于分离地研究岩土材料破坏前的失稳机制和失稳后的快速流动扩展。尝试以一种连续方法模拟完整的泥石流过程,仅用一个本构模型描述泥石流的起始、扩展和停滞。首先讨论了重力增大和基质吸力降低诱发泥石流的力学机制,描述了泥石流过程中岩土材料力学性质的弹塑性–黏性转变现象,对泥石流进行了黏弹塑性的全程模拟,并对挡土墙的冲击效应进行了启发性研究,证明了研究中所使用的本构模型可以准确地描述岩土材料的固流转化现象,数值方法可以很好地对均质连续介质进行大位移模拟。     

A hypoplastic model for clay and sand

The theory of hypoplasticity was developed initially for non-cohesive soils. However, sand and clay have many common properties; therefore arose the idea to extend the hypoplastic model to clay. The proposed model is able to describe the behaviour of cohesive soils with the incorporation of an appropriate structure tensor into the constitutive equation. This tensor is a stress-like internal parameter, also called back stress. This enables us to describe the behaviour of cohesive soils with the same material parameters for several states of consolidation and also to model barotropy and pycnotropy of sand. Numerical simulations of element tests are performed in order to check the performance of this hypoplastic model. Experimental data obtained with normally and overconsolidated clay and sand specimens with various densities are taken for comparison, and it is shown that the model is capable of describing the material behaviour of clay and sand. The determination of the material constants, the calibration method, is also presented in this paper.     

Incrementalization of a single hardening constitutive model for frictional materials

The governing equations for an elasto‐plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user‐defined module for finite element calculations. This isotropic, work‐hardening and ‐softening model employs a single yield surface, it incorporates non‐associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three‐dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26 :661). Copyright © 2002 John Wiley & Sons, Ltd.     

Implementation algorithm for a single hardening constitutive model for frictional materials

An advanced elasto‐plastic constitutive model for frictional materials, whose incremental version is presented in a companion paper (Int. J. Numer. Anal. Meth. Geomech., 2002; 26 :647), is implemented in a user‐defined material module. The general calculation strategy inside this module is presented and discussed, including the initial intersection of the yield surface and the techniques for updating of stresses and hardening modulus. Several integration schemes are implemented in the module and their capabilities in relation to the advanced, three‐dimensional constitutive model are evaluated. The forward Euler, modified Euler, and Runge–Kutta–Dormand–Prince integration schemes are explained in detail, compared, and evaluated in view of error tolerances and computational efficiency. Copyright © 2002 John Wiley & Sons, Ltd.