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.     

Uniqueness and existence in plasticity models for unsaturated soils

The paper investigates the mathematical structure of plasticity models for unsaturated soils and provides a strategy to capture the loss of uniqueness of the incremental solution upon loading and/or wetting paths. To derive bifurcation conditions in simple analytical form, the analysis is restricted to isotropic stress states. This choice has allowed the inspection of the most common classes of constitutive models through a unified notation, as well as the study of different forms of coupling between plasticity and state of saturation. It is shown that, similar to saturated soil plasticity, the loss of admissibility of the plastic solution is governed by critical values of the hardening modulus. At variance with the classical case, however, these moduli can be positive even if the plastic flow rule is associated (bifurcation in the hardening regime). The paper shows that such non-trivial features derive from hydro-mechanical coupling, i.e. they depend on the approach used to reproduce suction effects and evolving retention properties. In other words, although the problem of loss of uniqueness affects all classes of plasticity models for unsaturated soils, different constitutive assumptions may not have the same outcome in terms of bifurcation potential. As a result, new concepts are introduced to compare the mathematical robustness of the different constitutive approaches, as well as to interpret their predictions in the light of precise bifurcation criteria.     

A kinematic hardening based model for unsaturated soils considering different hydraulic conditions

At present, several of the existing elastoplastic constitutive models are adapted for describing the stress–strain behavior of unsaturated soils. However, most of them present certain limitations in this field. These limitations can be related to the basic model and/or added unsaturated state variables and formulations. In this regard, inability to model the hydro‐mechanical behavior in constant water (CW) conditions is an example of these limitations. In this paper, an advanced version of CJS model is selected for adaptation to the unsaturated states. Adaptation to unsaturated states is achieved in the framework of effective stress approach. Effective stress equation and unsaturated state variables are selected based on the recent research existing in the literature. The developed model is capable of describing the complex behavior of unsaturated soil in the CW condition in addition to predicting the behavior at failure and post–failure, nonlinear elastoplastic behavior at low levels of stress and strain (by selecting a very small elastic domain), as well as wetting and collapse behaviors. In order to validate the model, results of triaxial tests in CD and CW conditions are used. The validation results indicate the good capability of the proposed model. Behavior of the unsaturated soils during wetting is an important issue. For this reason, the model is also evaluated based on the results of wetting and collapse triaxial tests. A comparison between the tests and simulation results shows that the model is able to predict the soil behavior under the wetting path. Copyright © 2016 John Wiley & Sons, Ltd.     

Kinematic hardening plasticity formulation of small strain behaviour of soils

An objective of this paper is to demonstrate that the small strain model developed by the authors can be incorporated into the conventional kinematic hardening plasticity framework to predict pre‐failure defor mations. The constitutive model described in this paper is constituted by three elliptical yield surfaces in triaxial stress space. Two inner surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third surface is the modified Cam clay large‐scale yield surface. Within the linear elastic region, the soil behaviour is elastic with cross‐coupling between the shear and volumetric stress–strain components. Within the small strain region, the soil behaviour is elasto‐plastic, described by the kinematic hardening rule with an infinite number of loading surfaces defined by the incremental energy criterion. Within the large‐scale yield surface, the soil behaviour is elasto‐plastic, described by kinematic and isotropic hardening of the small strain region boundary. Since the yield surfaces have different shapes, the uniqueness of the plastic loading condition imposes a restriction on the ratio between their semi‐diameters. The model requires 12 parameters, which can be determined from a single consolidated undrained triaxial compression test. Copyright © 2000 John Wiley & Sons, Ltd.     

A plasticity constitutive model for unsaturated,anisotropic, nonexpansive soils

The paper describes and evaluates an incremental plasticity constitutive model for unsaturated, anisotropic, nonexpansive soils (CMUA). It is based on the modified Cam-Clay (MCC) model for saturated soils and enhances it by introducing anisotropy (via rotation of the MCC yield surface) and an unsaturated compressibility framework describing a double dependence of compressibility on suction and on the degree of saturation of macroporosity. As the anisotropic and unsaturated features can be activated independently, the model is downwards compatible with the MCC model. The CMUA model can simulate effectively: the dependence of compressibility on the level of developed anisotropy, uniqueness of critical state independent of the initial anisotropy, an evolving compressibility during constant suction compression, and a maximum of collapse. The model uses Bishop's average skeleton stress as its first constitutive variable, favouring its numerical implementation in commercial numerical analysis codes (eg, finite element codes) and a unified treatment of saturated and unsaturated material states.     

非饱和土的清华弹塑性模型

为研究土在非饱和增湿情况下的应力、应变和强度关系,提出将含水率引入清华模型的硬化参数中建立非饱和土的清华弹塑性模型。通过在干土中掺加冰屑的方法进行增湿试验,表明该模型可以预测不同含水率的非饱和土的应力-变形和强度关系,从天然风干状态增湿到其他含水率的应力-应变全过程的计算结果也与试验结果相符合。将含水率直接引入弹塑性模型而不去研究复杂的基质吸力,可能是非饱和土本构模型工程应用的一条简便途径。     

Thermo-elastoplastic constitutive model for unsaturated soils

This study presents a simple approach to modelling the effect of temperature on the deformation and strength of unsaturated/saturated soils by using the average skeleton stress and degree of saturation. The concept of thermo-induced equivalent stress is introduced to consider the influence of temperature on the pre-consolidated stress. A skeleton stress–saturation framework is applied to enable the model to describe the thermo-elastoplastic behaviour of both unsaturated and saturated soils, as the skeleton stress can smoothly shift to Terzaghi’s effective stress if saturation changes from the unsaturated to the saturated condition. The new model only employs seven parameters, of which five parameters are the same as those used in the Cam-Clay model. The other two parameters can be easily determined by oedometer tests and simple thermo-mechanical tests. Numerical simulations of isotropic loading tests and triaxial shear tests under different conditions are conducted to illustrate the performance of the proposed model. By comparing with experimental temperature controlled oedometer tests and triaxial tests, it is confirmed that the proposed model is able to capture the thermo-mechanical behaviour of unsaturated/saturated normally and over-consolidated soils with a set of unified parameters.     

考虑温度影响的重塑非饱和膨胀土非线性本构模型

以非饱和土的非线性模型为基础,通过对土性参数的修正和考虑温度本身引起的土的变形,建立了考虑温度效应的重塑非饱和膨胀土的本构模型。该模型包括土骨架的本构关系和水量变化的本构关系两个方面,涉及18个参数,都可用非饱和土三轴试验确定。共做了13个重塑非饱和膨胀土温控三轴试验,分析了温度对土的强度和变形的影响,研究了模型参数的变化规律。     

非饱和土的水分特征曲线的分形模型

水分特征曲线的分形模型以分为三类：土颗粒分布的分形模型、土体孔隙表面的分形模型和土体孔隙分布的分形模型。根据土孔隙分布的分形模型，提出了水分特征曲线的通用表达式。水分特征曲线的通用表达不仅能很好地预测近饱和状态和干土状态时的水分特征曲线，也能用相同的分维估算水分特征曲线的脱水曲线和吸水曲线。     

非饱和土广义有效应力原理

综述了非饱和土有效应力的沿革,并就非饱和土有效应力的研究和发展中存在的问题进行了讨论。基于多相孔隙介质理论推导得到的变形功的表达式,提出了非饱和土广义有效应力原理。该原理认为,由非饱和土中的单应力变量的有效应力或双应力变量理论很难唯一地确定非饱和土的变形和强度。广义有效应力原理实质上就是要综合考虑影响非饱和土变形和强度的三种广义应力以及与其对偶的广义变形,给出考虑因素更为全面、理论基础更为坚实的广义有效应力原理。它为非饱和土基本性质的研究和本构方程的建立奠定了坚实而科学的理论基础。     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part 1: Saturated state

The behavior of granular materials is known to depend on its loose or dense nature, which in turns depends both on density and confining pressure. Many models developed in the past require the use of different sets of constitutive parameters for the same material under different confining pressures. The purpose of this paper is to extend a basic generalized plasticity model for sands proposed by Pastor, Zienkiewicz and Chan by modifying the main ingredients of the model flow—rule, loading–unloading discriminating direction and plastic modulus—to include a dependency on the state parameter. The proposed model is tested against the available experimental data on three different sands, using for each of them a single set of material parameters, finding a reasonably good agreement between experiments and predictions. Copyright © 2010 John Wiley & Sons, Ltd.     

Implicit numerical integration for a kinematic hardening soil plasticity model

Soil models based on kinematic hardening together with elements of bounding surface plasticity, provide a means of introducing some memory of recent history and stiffness variation in the predicted response of soils. Such models provide an improvement on simple elasto‐plastic models in describing soil behaviour under non‐monotonic loading. Routine use of such models requires robust numerical integration schemes. Explicit integration of highly non‐linear models requires extremely small steps in order to guarantee convergence. Here, a fully implicit scheme is presented for a simple kinematic hardening extension of the Cam clay soil model. The algorithm is based on the operator split methodology and the implicit Euler backward integration scheme is proposed to integrate the rate form of the constitutive relations. This algorithm maintains a quadratic rate of asymptotic convergence when used with a Newton–Raphson iterative procedure. Various strain‐driven axisymmetric triaxial paths are simulated in order to demonstrate the efficiency and good performance of the proposed algorithm. Copyright © 2001 John Wiley & Sons, Ltd.     

A novel multifunctional apparatus for testing unsaturated soils

Acta Geotechnica - There are limited studies in the development of testing apparatus on unsaturated soils due to the complex structure, tedious calibration process, and large demands on test time...     

A fully coupled simple model for unsaturated soils

Different phenomena influence the strength and volumetric behavior of unsaturated soils. Among the most important are suction hardening, hydraulic hysteresis, and the influence of volumetric strain on the soil-water retention curves. Fully coupled hydro-mechanical models require including all three phenomena in their constitutive relationships. Among these phenomena, suction hardening is the most influencing as it determines the apparent preconsolidation stress, the position of the loading-collapse yield surface, and the shift of both the isotropic consolidation and the critical state lines. In this paper, a fully coupled hydro mechanical model is presented. It is based on the modified Cam-Clay model but includes a yield surface with anisotropic hardening that takes account of the shift of the critical state line with suction. For highly overconsolidated materials, the sub-loading surface concept has been included in order to increase the precision of the model for these materials. The shift of the retention curves produced by volumetric strains is simulated using a hydraulic model based on the grain and current pore size distribution of the soil.     

Work input for unsaturated soils considering interfacial effects

In this research, the interfacial energy is taken into account in the deformation work for unsaturated soils. Based on porous media theory, the thermodynamic balance equations for each phase and the interface are used to derive the work input for unsaturated soils. The work input equation serves as the basis and starting point for the choice of stress state variables, based on which the conjugate stresses and strain increments are derived. The influences of the interfaces on the effective stress and the constitutive law for the liquid phase are then discussed based on the work input equation. The effective stress can be expressed as Bishop's type, and the effective stress parameter is shown to be a function of both the degree of saturation and the interfacial area. The constitutive law for the liquid phase under dynamic condition is also presented. The relationship among interfacial area, saturation, and capillary pressure is proposed to calculate the value of the effective stress. Experimental data obtained from literature are used to validate the proposed model equations. Results show that our findings are in accordance with the existing research. Unlike the phenomenal study, our research has a rigorous theoretical basis, which lays a foundation for further research of unsaturated soils considering the interfacial effects.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

A hypoplastic model for mechanical response of unsaturated soils

A new constitutive model is developed for the mechanical behaviour of unsaturated soils based on the theory of hypoplasticity and the effective stress principle. The governing constitutive relations are presented and their application is demonstrated using several experimental data from the literature. Attention is given to the stiffening effect of suction on the mechanical response of unsaturated soils and the phenomenon of wetting‐induced collapse. All model parameters have direct physical interpretation, procedures for their quantification from test data are highlighted. Quantitative predictions of the model are presented for wetting, drying and constant suction tests. Copyright © 2008 John Wiley & Sons, Ltd.     

Constitutive modeling of unsaturated aggregated soils

A coupled water retention–mechanical constitutive model for unsaturated aggregated soils is presented here. Based on the multi‐scale experimental results, the model incorporates the inter‐particle bonding, fabric and partial saturation effects in a single framework. It is formulated within the framework of hardening elasto‐plasticity and is based on the critical state concept. Prior to model validation, we evaluate the model parameters and propose determination procedures for the main new parameters. Finally, the model is examined for its capability in simulating the experimental results of aggregated and bonded soils. Results of these simulations show that the model addresses the most features arising from the combined effects of soil structure and partial saturation. Copyright © 2010 John Wiley & Sons, Ltd.     

On constitutive modelling of unsaturated soils

The paper presents a review of constitutive modelling of unsaturated soils. After a brief historical perspective, a number of existing constitutive models are classified and discussed according to the type of stress variables adopted in their formulation. Afterwards, attention is given to recent developments in the proposal of coupled hydraulic-mechanical models and the possibility of casting them in a sound thermodynamical framework. Finally, a double structure model for expansive soils is described. The incorporation of microstructural considerations and its use as a platform for incorporating the influence of new variables are highlighted.