An anisotropic elastoplastic model for soft clays based on logarithmic contractancy

A new constitutive model for soft structured clays is developed based on an existing model called S‐CLAY1S, which is a Cam clay type model that accounts for anisotropy and destructuration. The new model (E‐SCLAY1S) uses the framework of logarithmic contractancy to introduce a new parameter that controls the shape of the yield surface as well as the plastic potential (as an assumed associated flow rule is applied). This new parameter can be used to fit the coefficient of earth pressure at rest, the undrained shear strength or the stiffness under shearing stress paths predicted by the model. The improvement to previous constitutive models that account for soil fabric and bonding is formulated within the contractancy framework such that the model predicts the uniqueness of the critical state line and its slope is independent of the contractancy parameter. Good agreement has been found between the model predictions and published laboratory results for triaxial compression tests. An important finding is that the contractancy parameter, and consequently the shape of the yield surface, seems to change with the degree of anisotropy; however, further study is required to investigate this response. From published data, the yield surface for isotropically consolidated clays seems ‘bullet’ or ‘almond’ shaped, similar to that of the Cam clay model; while for anisotropically consolidated clays, the yield surface is more elliptical, like a rotated and distorted modified Cam clay yield surface. © 2015 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Predictions of large stress reversals in true triaxial tests on cross‐anisotropic sand

A rotational kinematic hardening constitutive model with the capability of predicting the behavior of soil during three‐dimensional stress reversals has been developed. An existing elasto‐plastic constitutive model, the Single Hardening Model, utilizing isotropic hardening serves as the basic framework in these formulations. The framework of the kinematic hardening model was discussed in a companion paper. The previously proposed cross‐anisotropic Single Hardening Model is added to the present kinematic hardening mechanism to capture inherent anisotropy of sands in addition to the stress reversals. This model involves 13 parameters, which can be determined from simple laboratory experiments, such as isotropic compression, drained triaxial compression and triaxial extension tests. The results from a series of true triaxial tests with large three‐dimensional stress reversals performed on medium dense cross‐anisotropic Santa Monica Beach sand are employed for comparison with predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

复杂应力条件下土体各向异性及其建模思路

由于加荷方式不同,土体在复杂应力状态下在各主应力方向上应力-应变关系表现出显著应力各向异性,在常规三轴试验基础上,采用经典弹塑性理论各向同性土体模型对此不能合理描述。通过真三轴试验,总结应力各向异性柔度矩阵规律,结合试验规律进行相应理论研究,用非线性各向异性弹性矩阵代替弹塑性模型的弹性矩阵,用具有各向异性屈服准则的弹塑性模型描述塑性部分,建立非线性各向异性弹性-塑性模型,可以改善柔度矩阵矩阵形态,反映复杂应力状态下土体应力各向异性特征。     

Constitutive modeling of the destructuration and anisotropy of natural soft clay

The mechanical behavior of natural clays is affected by their inherent anisotropy and metastable soil structure. A simple hierarchical model that considers initial anisotropy and destructuration was formulated within the framework of critical state soil mechanics. In the proposed model, stress sensitivity and a destructuration index were introduced to account for the degree of bonding and the rate of destructuration, respectively. An inclined yield surface was used to incorporate the effect of the initial anisotropy. The proposed model can be degenerated to the Modified Cam Clay model by setting the initial stress sensitivity equal to unity and using a horizontal yield surface. Reasonable agreement between the model simulations and the experimental results on a variety of stress paths demonstrated that the proposed model can capture well the deformation behavior of natural clay and reconstituted soil. The model was implemented into the finite element program for the numerical analysis of an embankment on soft clay improved with prefabricated vertical drains. The numerical predictions were compared with the field-measured data in terms of embankment settlement. Additionally, the numerical simulations were analyzed in terms of horizontal displacements, excess pore water pressure, mean effective stress and volumetric strain. All of the simulations and comparisons indicate the importance of considering the effects of plastic anisotropy, interparticle bonding and destructuration caused by loading beyond yield stress and field disturbance in analyzing the behavior of an embankment on natural soft clay.     

A unified bounding surface plasticity model for unsaturated soils

A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non‐associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress–strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam‐Clay‐based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress–strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance of constitutive models in predicting behavior of remolded clay

The performance of several soil constitutive models was evaluated by comparing experimental results and simulated behavior of a medium plasticity clay. Input parameters for the soil constitutive models were obtained from triaxial compression and extension tests on normally and overconsolidated medium plasticity clay. The soil models employed for this study were the Cam Clay, Modified Cam Clay, 3-SKH, and S-CLAY1 models. In order to investigate the influence of some of the input parameters on the performance of the models, sensitivity analyses were also performed. The comparisons demonstrate that the Cam Clay model was able to predict the normally consolidated compressive behavior of medium plasticity clay. Both 3-SKH and Cam Clay models were able to produce acceptable predictions for stress?Cstrain and stress path behavior for overconsolidated compression of the soil. The 3-SKH model did not perform satisfactorily for predicting pore pressure variations, while the Cam Clay model demonstrated fairly acceptable predictions. For the normally consolidated reduced extension test, the Modified Cam Clay and S-CLAY1 models performed better than the Cam Clay and 3-SKH models in predicting the stress?Cstrain curve, pore pressure variations, and stress path.     

Kinematic hardening predictions of large stress-reversals in 3-D test on loose sand

A rotational kinematic hardening constitutive model with the capability of predicting the behavior of soil during 3-D stress-reversals has been developed. An existing elasto-plastic constitutive model, the Single Hardening Model, utilizing isotropic hardening serves as the basic framework in these formulations. To this framework is added the capability of handling cross-anisotropic behavior as well as the kinematic hardening mechanism to capture inherent anisotropy of the sand in addition to the large stress-reversals. The model involves thirteen parameters, which can be determined from simple laboratory experiments, such as isotropic compression, drained triaxial compression and triaxial extension tests. The results from a series of true triaxial tests with large stress-reversals performed on loose cross-anisotropic Santa Monica Beach sand are employed for comparison with predictions.     

Model identification and parameter estimation of elastoplastic constitutive model by data assimilation using the particle filter

Data assimilation, using the particle filter and incorporating the soil‐water coupled finite element method, is applied to identify the yield function of the elastoplastic constitutive model and corresponding parameters based on the sequential measurements of hypothetical soil tests and an actual construction sequence. In the proposed framework of the inverse analysis, the unknowns are both the particular parameter within the exponential contractancy model, n_E, which parameterizes various shapes for the yield function of the competing constitutive models, including the original/the modified Cam‐Clay models and in‐between models and the parameters of the corresponding constitutive model. An appropriate set, consisting of the yield function of the constitutive model and the parameters of the constitutive model, can be simultaneously identified by the particle filter to describe the most suitable soil behavior. To examine the validity of the proposed procedure, hypothetical and actual measurements for the displacements of a soil specimen were obtained for consolidated and undrained tests through a synthetic FEM computation and for consolidated and drained tests, respectively. After examining the applicability of the proposed procedure to these test results, the present paper then focuses on the actual measured data, ie, the settlement behavior including the lateral deformation of the Kobe Airport Island constructed on reclaimed land.     

Generalized strain probing of constitutive models

Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimization framework for calibration of constitutive models enhanced by neural networks

A two‐level procedure designed for the estimation of constitutive model parameters is presented in this paper. The neural network (NN) approach at the first level is applied to achieve the first approximation of parameters. This technique is used to avoid potential pitfalls related to the conventional gradient‐based optimization techniques, considered here as a corrector that improves predicted parameters. The feed‐forward NN (FFNN) and the modified Gauss–Newton algorithms are briefly presented. The proposed framework is verified for the elasto‐plastic modified Cam Clay model that can be calibrated based on standard triaxial laboratory tests, i.e. the isotropic consolidation test and the drained compression test. Two different formulations of the input data to the NN, enhanced by a dimensional reduction of experimental data using principal component analysis, are presented. The determination of model characteristics is demonstrated, first on numerical pseudo‐experiments and then on the experimental data. The efficiency of the proposed approach by means of accuracy and computational effort is also discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Constitutive analysis of the mechanical anisotropy of Opalinus Clay

This paper aims to analyse the anisotropic features of behaviour of Opalinus Clay using the theory of plastic multi-mechanisms. The results of triaxial tests conducted with different load levels and directions showed that the mechanical behaviour of this shale is cross-anisotropic. The stiffer samples are those in which the loading direction is parallel to the bedding plane. This indicates that the preconsolidation stress depends on the orientation of the load with respect to the fabric of Opalinus Clay. It is proposed to interpret the observed cross-anisotropy with an elastoplastic model based on four plastic strain mechanisms that may be successively mobilised depending on the loading direction. The predicted stress–strain responses vary according to the directions of the space as a result of the hardening process, depending on the number of plastic strain mechanisms that have been mobilised. The numerical predictions show overall good agreement with the experimental data in terms of deviatoric stress versus axial strain, demonstrating that multi-mechanism plasticity is a suitable constitutive tool for the interpretation of the mechanical anisotropy of this shale.     

On some advanced thermo‐mechanical models for saturated clays

This paper aims to evaluate the performance of several recent constitutive models in simulating the thermo‐mechanical behaviour of saturated clays. A classic thermo‐mechanical test on natural Boom Clay, commonly used in constitutive modelling, was first clarified. Different methods commonly used to measure volumetric strain in drained heating tests were then discussed. Model evaluation was performed in terms of thermodynamic and elasto‐plastic requirements. The capability of the models to capture the observed behaviour was assessed on the basis of the experimental evidence. It was shown that all the models provide reasonable predictions of the thermo‐mechanical behaviour of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. Copyright © 2013 John Wiley & Sons, Ltd.     

考虑饱和黏土初始各向异性的循环边界面塑性模型

天然土体的初始各向异性通常可对其后继循环特性产生显著影响。现有考虑循环载荷作用的土体弹塑性模型,往往采用类似修正剑桥模型的椭圆形屈服面,已有研究表明,该椭圆形屈服面因其拉伸弹性区域偏大,针对天然K0固结状态的土体,其计算精度较差。基于新近提出的广义各向同性硬化准则,在边界面方程中引入初始各向异性张量,并采用空间滑动面破坏准则（SMP）的变换应力法,建立了能考虑饱和黏土初始各向异性的循环边界面塑性模型。分别针对等压和偏压固结的饱和黏土静、动三轴试验进行模拟,结果表明,该模型能合理反映土体的初始各向异性及其后继循环动力特性。     

Probabilistic yielding and cyclic behavior of geomaterials

In this paper, the novel concept of probabilistic yielding is used for 1‐D cyclic simulation of the constitutive behavior of geomaterials. Fokker–Planck–Kolmogorov equation‐based probabilistic elastic–plastic constitutive framework is applied for obtaining the complete probabilistic (probability density function) material response. Both perfectly plastic and hardening‐type material models are considered. It is shown that when uncertainties in material parameters are taken into consideration, even the simple, elastic‐perfectly plastic model captures some of the important features of geomaterial behavior, for example, modulus reduction with cyclic strain, which, deterministically, is only possible with more advanced constitutive models. Furthermore, it is also shown that the use of isotropic and kinematic hardening rules does not significantly improve the probabilistic material response. Copyright © 2010 John Wiley & Sons, Ltd.     

A hierarchical approach for constitutive modelling of geologic materials

A hierarchical concept is proposed for the development of constitutive models to account for various factors that influence behaviour of (geologic) materials. It permits evolution of models of progressively higher grades from the basic model representing isotropic hardening with associative behaviour. Factors such as non-associativeness and induced anisotropy due to friction and cyclic loading, and softening are introduced as corrections or perturbations to the basic model. The influence of these factors is captured through non-associativeness manifested by deviation from normality of the plastic strain increments to the yield surface, F. Details of four models: isotropic hardening with associative behaviour, isotropic hardening with non-associative behavioural anisotropic hardening and strain-softening with a damage variable are presented. They are verified with respect to laboratory multiaxial test data under various paths of loading, unloading and reloading for typical soils, rock and concrete. The proposed concept is general, yet sufficiently simplified in terms of physical understanding, number of constants and their physical meanings, determination of the constants and implementation.     

Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

Geomaterials such as soils and rocks are inherently anisotropic and sensitive to temperature changes caused by various internal and external processes. They are also susceptible to strain localization in the form of shear bands when subjected to critical loads. We present a thermoplastic framework for modeling coupled thermomechanical response and for predicting the inception of a shear band in a transversely isotropic material using the general framework of critical state plasticity and the specific framework of an anisotropic modified Cam–Clay model. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Subsequently, stress‐point simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermomechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation. Copyright © 2016 John Wiley & Sons, Ltd.     

Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects

This paper is devoted to develop a theoretical framework to predict the macroscopic transversely isotropic elastoplastic behavior of clay‐like material, which is viewed as a porous polycrystal. We consider evolutions of two local plastic mechanisms of grains and interface simultaneously, for which a Schmid criterion is used for the strength of sheet‐like grains and a Tresca criterion for the strength of interfaces between particles. By adapting the standard incremental method, we propose firstly a classic self‐consistent model, which does not consider the effect of interface, then a generalized self‐consistent model in which the solid phase is represented by laminated (or isotropic) spherical grains surrounded by interfaces. Comparisons of numerical predictions between these two methods are performed and have demonstrated the validity of the generalized self‐consistent model taking account of interface effects. Numerical simulations of uniaxial compression tests have shown that the macroscopic elastoplastic behavior of polycrystalline (clay‐like) material can be successfully predicted by the way of considering the two local plastic mechanisms at microscopic scale. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of the plastic potential in boundary value problems involving plane strain deformation

A large proportion of the constitutive models currently employed in Geomechanics are based on the theory of plasticity. Owing to the limitations of the data obtained from conventional testing equipment, arbitrary assumptions are often made about the behaviour of the material in generalized stress space. In this paper it is shown that the Lode angle of the stress state at failure in plane strain deformation is dependent on the shape adopted for the plastic potential. The influence of the shape of the plastic potential in the deviatoric plane on the predicted behaviour of two boundary value problems both prior to and at failure is then considered. In both cases a form of the Modified Cam Clay model is employed to describe the soil behaviour, and numerical predictions are obtained using a finite element computer code. For drained situations it is shown that the Lode angle of the stress state at failure has a dominating influence on the predicted behaviour. However, for undrained cases the effects are not so important as long as the correct undrained strength at failure is enforced.