The subloading isotropic plasticity as a variable modulus model

The subloading concept is an extension of mathematical plasticity which defines an internal surface to the conventional yield surface. It is indeed a versatile approach, especially for the modelling of soils under quasi-static cycles with smooth transitions from pure elastic to elastoplastic behaviour. For the case of isotropic hardening models, this paper demonstrates that the subloading isotropic plasticity is equivalent to a variable modulus approach and therefore a simpler and equivalent methodology can be adopted instead. In addition to demonstrating this equivalence, an alternative formulation that was presented elsewhere and that uses only one surface is briefly discussed. The alternative formulation can then be easily applied to popular models for soils such as the Cam clay model. Finally, some numerical predictions are presented in order to illustrate the capabilities of the subloading isotropic plasticity and the corresponding variable modulus approach.     

一种适用于饱和黏土循环动力分析边界面塑性模型的隐式积分算法

修正了传统隐式回映算法,建立了适用于饱和黏土循环动力分析的边界面塑性模型的完全隐式积分格式。该模型基于无弹性域概念和临界状态理论,采用各向同性、运动硬化准则、旋转的边界面,并引入表征土体结构损伤和重塑程度的损伤变量以反映循环载荷作用下饱和黏土的各向异性、刚度、强度软化及塑性变形累积等特征。针对等压固结 和偏压固结 的饱和高岭黏土的不排水三轴试验进行模拟,采用不同的应变增量步长进行计算,并与试验数据对比,结果表明,修正隐式回映算法应用于该类边界面模型的合理性、积分格式的精确性和稳定性;另外,结合有限元软件自动时间步长的增量迭代解法,对饱和黏土应力控制的不排水动三轴试验进行预测,结果表明,修正的适用于该边界面的塑性模型隐式回映算法可以得到比较合理的数值分析结果,能够反映饱和黏土的循环刚度的退化和强度的弱化等动力特性。     

Modeling the behavior of sandstone based on generalized plasticity concept

With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre‐peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post‐peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

A Generalized Plasticity-Based Model for Sandstone Considering Time-Dependent Behavior and Wetting Deterioration

Based on the concept of generalized plasticity, this study proposes a constitutive model to describe the time-dependent behavior and wetting deterioration of sandstone. The proposed model (1) exhibits nonlinear elasticity under hydrostatic and shear loading, (2) follows the associated flow rule for viscoplastic deformation, (3) adopts a creep modulus that varies with the stress ratio, (4) considers the primary and secondary creep behaviors of rock, and (5) considers the effect of wetting deterioration. This model requires 13 material parameters, comprising 3 for elasticity, 7 for plasticity, and 3 for creep. All parameters can be determined easily by following the suggested procedures. The proposed model is first validated by comparison with triaxial tests of sandstone under different hydrostatic stress and cyclic loading conditions. In addition, the model is versatile in simulating time-dependent behavior through a series of multistage creep tests. Finally, to consider the effects of wetting deterioration, triaxial and creep tests under dry and water-saturated conditions are simulated. Comparison of the simulated and experimental data shows that the proposed model can predict the behavior of sandstone in dry and saturated conditions.     

A general basis for yield,failure and potential functions in plasticity

A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.     

A J2‐plasticity model based on bounding surface concept

This article presents the development of a J₂ small strain plasticity model based on bounding surface concept, along with numerical examples to demonstrate model behaviors and identification of model parameter using laboratory test data. The model is motivated by the need for simulating permanent deformation accumulation of asphalt concrete mixtures, which leads to rutting in flexible pavements under repeated traffic loading. The proposed model accounts for the observation that rutting is mostly caused by shearing and takes advantage of the fact that bounding surface concept allows for the progressive accumulation of plastic deformation under constant amplitude loading condition. Analytical solutions are given for typical laboratory testing conditions. The model can be calibrated using repeated simple shear test data that are typically available for asphalt concrete mixtures. It is shown that the model is easy to use and provides a promising alternative for modeling permanent deformation accumulation in materials subjected to repetitive (cyclic) loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Bearing capacity factor, <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">γ</Emphasis></Subscript>, for unsaturated soils by ZEL method

Bearing capacity of foundations is often determined for saturated state of the soil, regarding its simple and conservative results. This assumption, however, results in very uneconomic and overconservative design for a wide range of climates in the world. In this paper, plasticity equations were employed and extended for unsaturated soils to establish a theoretical approach to investigate the bearing capacity of unsaturated soils. It is achieved by combining the concept of effective stress and plasticity equations in terms of effective stress in unsaturated soils. The advantage of Bishop’s (4) effective stress concept was employed to simplify the equations. The equations were then transformed onto the zero extension lines directions to generalize this method for both associative and non-associative problems by which both stress and velocity field can be determined for unsaturated soils. A computer code was also developed to solve the relatively complex plasticity equations for a wide range of soil friction angles and matric suctions to compute the corresponding bearing capacity factor, N _γ , for strip foundations with smooth and rough base. This factor seems to be one of the major contributors in the bearing capacity of shallow foundations. The results have been presented in design charts and theoretical equations.     

A flow theory for soil: Concept of multiple neutral loading surfaces

A flow theory for soils is proposed which diverts considerably from the classical theory of plasticity. The theory is based on the concept of multiple loading surfaces defining neutral states for which irreversible deformation cease to exist. The constitutive relation has an incremental nature and the ratios of the components of plastic strain rate are functions of both the current stress and the stress rate. The concept of the yield locus is no longer involved in the formulation.     

A unified method to predict diffuse and localized instabilities in sands

A simplified method to analyse diffuse and localized bifurcations of sand under drained and undrained conditions is presented in this paper. This method utilizes results from bifurcation analysis and critical state plasticity theory to detect the onset of pure and dilatant shear band formation, static liquefaction and drained shear failures systematically. To capture the soil collapse observed in experiments, the instability state line concept originated by Chu, Lo and Lee in 1993 is adopted. Emphasis is given to examine how the presence of pore-fluid may facilitate or delay instability after yielding occurs. The predictions of instabilities are compared with experimental data from triaxial compression tests on Toyoura and Changi sands.     

A macro‐element for a circular foundation to simulate 3D soil–structure interaction

This paper presents a non‐linear interface element to compute soil–structure interaction (SSI) based on the macro‐element concept. The particularity of this approach lies in the fact that the foundation is supposed to be infinitely rigid and its movement is entirely described by a system of global variables (forces and displacements) defined in the foundation's centre. The non‐linear behaviour of the soil is reproduced using the classical theory of plasticity. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. The macro‐element is appropriate for modelling the cyclic or dynamic response of structures subjected to seismic action. More specifically, the element is able to simulate the behaviour of a circular rigid shallow foundation considering the plasticity of the soil under monotonic static or cyclic loading applied in three directions. It is implemented into FedeasLab, a finite element Matlab toolbox. Comparisons with experimental monotonic static and cyclic results show the good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Phenotypic plasticity of Acanthoscaphites tridens (Late Cretaceous ammonites): additional data

The concept of phenotypic plasticity of the temporal species Acanthoscaphites tridens s. str., as recently proposed by myself is elaborated upon, in response to issues raised in a commentary to the original paper. The terms phenomorphic class and dominant phenotype are explained in greater detail, as well as the evaluation of phenotypic plasticity in studies for extinct species.     

Constitutive modeling of dense gravelly soils subjected to cyclic loading

A constitutive model for dense gravelly soils was developed to reproduce their responses under cyclic loadings. Its application aims at nonlinear dynamic analyses of earth structures involving gravelly soils, such as rockfill dams and railroad ballasts. The framework of generalized plasticity was modified to incorporate the concept of stress distance for better simulation of unloading and reloading responses. It was then combined with the theory of critical state soil mechanics to develop the constitutive model. The model has the following important features: unified simulation of particle breakage through translating critical state line, smooth transition from unloading to reloading in the stress space, and proper modeling of cyclic hysteresis, cyclic densification, and cyclic hardening of dense gravelly soils. Most of the model parameters can be obtained through simple calculation using conventional triaxial test results, and their calibration process was discussed. The model was used to simulate the cyclic responses of three gravelly soils with satisfactory accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

Laboratory Investigation of the Resistance of Tailings and Natural Sediments to Cyclic Loading

A number of cyclic triaxial tests were carried out on mine tailings and natural sediment samples under undrained conditions to investigate their resistance to cyclic loading. The tests were performed on more than 100 samples with a cyclic shear stress ratio ranging from 0.10 to 0.40 under varying void ratio and the same confining pressure. It was observed that the axial strain and excess pore water pressure increased with the number of loading cycles while the effective stress decreased with increasing number of loading cycles. The liquefaction resistance of the tailings was also observed to be higher than that of natural soils with similar particle size distribution, void ratio and plasticity index. It was observed that the influence of specific gravity on the cyclic strength of mine tailings is significant. The results showed that the cyclic resistance of the tailings was not strongly influenced by plasticity index for low plasticity tailings. A boundary relationship between void ratio and normalized cyclic resistance ratio was established based on the results.     

冻融循环对不同塑性指数路基土弹性模量的影响研究

在季节性冻土区,不同状态（塑性指数,围压等）路基土在通车运营期间经历冻融循环后,其物理力学性质会发生变化,但目前针对冻融循环对其的影响研究还不够广泛和深入,不能给季冻区路基设计提供准确的数据支持,故路基设计时并未将这种变化考虑其中,只取设计前期所采土样的试验值。取季节性冻土区3种不同塑性指数路基土,在室内采用最佳含水率制备成最大压实度试样,在封闭条件下经历0～7次完整冻融循环过程后,进行不同围压下的三轴压缩试验,在偏应力-应变曲线中通过直线段应力-应变关系得到弹性模量数据,结果表明,同种土相同冻融循环次数下,弹性模量随围压增加而增加;相同围压下弹性模量随冻融循环次数基本呈下降趋势。采用指数函数对所有弹性模量数据进行多元非线性拟合,建立不同塑性路基土弹性模量与围压及冻融循环次数的关系,拟合效果理想,可为缺乏相关资料的季冻区路基设计提供参考。     

A critical state two-surface plasticity model for gravelly soil-structure interfaces under monotonic and cyclic loading

An elasto-plastic model is proposed for modeling the constitutive behavior of the interface between gravelly soils and structural materials. This model is based on the two-surface plasticity formulation and it is compatible with the concept of critical state soil mechanics. The model requires the same set of eight calibration parameters for predicting the monotonic and cyclic responses of both loose and dense interfaces. The model simulates cyclic densification, shear degradation and the effects of normal pressure, soil density, and stress path. The performance of the proposed constitutive model is validated by tests data under different normal stresses and boundary conditions.     

砂土多机构边界面塑性模型及其试验验证

根据Iai多重剪切机构塑性模型及边界面塑性模型的特点,建立了一个砂土多机构边界面塑性模型。该模型将土复杂的变形机理分解为体积机理和一系列简单的剪切机理。用边界面弹塑性模型模拟多重剪切机构塑性模型中虚拟单剪机构,避免了Iai多重剪切机构塑性模型在利用修正Masing准则模拟虚拟单剪应力-应变关系时确定比例参数的复杂性。根据大量试验资料,建立了液化面参数与归一累积剪切功的关系,能够用较少的参数很好地建立有效应力路径。由于多重机理的特性,该模型能够模拟复杂荷载作用下主应力轴偏转的影响。试验结果表明,应用该模型的计算结果与试验结果有较好的一致性。     

Creep in rock as a stochastic process

The heterogeneous character of rock suggests the use of statistical mechanics for the formulation of models of plasticity and creep. A stochastic creep model which allows for large variations in strength and size of the involved rock mass is outlined. The model, which is analogous to a previously developed concept for clastic materials, is shown to account rather well for typical creep behaviour of rock at moderate stresses and temperatures. Thus, it yields the often observed linear relation between the creep strain and the logarithm of time.     

Generalized plasticity and the modelling of soil behaviour

The paper outlines the theory of generalized plasticity in which yield and plastic potential surfaces need not be explicitly defined, and shows how a very effective general model describing the behaviour of sands and of clays under monotonic or transient loading can be developed. The model is currently one of the simplest and yet one of the most effective ones for describing the full range of behaviour. The hierarchical structure of the model limits the number of parameters which have to be experimentally determined for a given material to those strictly necessary for the problem at hand. A discussion of currently used models is included.